Template Credit: Adapted from a template made available by Dr. Jason Brownlee of Machine Learning Mastery. [https://machinelearningmastery.com/]

SUMMARY: The purpose of this project is to construct a prediction model using various machine learning algorithms and to document the end-to-end steps using a template. The Human Activities and Postural Transitions dataset is a classic multi-class classification situation where we are trying to predict one of the 12 possible outcomes.

INTRODUCTION: The research team carried out experiments with a group of 30 volunteers who performed a protocol of activities composed of six basic activities. There are three static postures (standing, sitting, lying) and three dynamic activities (walking, walking downstairs and walking upstairs). The experiment also included postural transitions that occurred between the static postures. These are stand-to-sit, sit-to-stand, sit-to-lie, lie-to-sit, stand-to-lie, and lie-to-stand. All the participants were wearing a smartphone on the waist during the experiment execution. The research team also video-recorded the activities to label the data manually. The research team randomly partitioned the obtained data into two sets, 70% for the training data and 30% for the testing.

In the current iteration Take1, the script will focus on evaluating various machine learning algorithms and identifying the model that produces the best overall metrics. Because the dataset has many attributes that are collinear with other attributes, we will eliminate the attributes that have a collinearity measurement of 99% or higher. Iteration Take1 will establish the baseline performance for accuracy and processing time.

ANALYSIS: In the current iteration Take1, the baseline performance of the machine learning algorithms achieved an average accuracy of 89.80%. Two algorithms (Linear Discriminant Analysis and eXtreme Gradient Boosting) achieved the top accuracy metrics after the first round of modeling. After a series of tuning trials, eXtreme Gradient Boosting turned in the top overall result and achieved an accuracy metric of 98.59%. By using the optimized parameters, the eXtreme Gradient Boosting algorithm processed the testing dataset with an accuracy of 93.67%, which was below the training data and possibly due to over-fitting.

From the model-building perspective, the number of attributes decreased by 108, from 561 down to 453.

CONCLUSION: For this iteration, the eXtreme Gradient Boosting algorithm achieved the best overall results. For this dataset, we should consider using the eXtreme Gradient Boosting algorithm for further modeling or production use.

Dataset Used: Smartphone-Based Recognition of Human Activities and Postural Transitions Data Set

Dataset ML Model: Multi-class classification with numerical attributes

Dataset Reference: https://archive.ics.uci.edu/ml/datasets/Smartphone-Based+Recognition+of+Human+Activities+and+Postural+Transitions

The project aims to touch on the following areas:

  1. Document a predictive modeling problem end-to-end.
  2. Explore data cleaning and transformation options
  3. Explore non-ensemble and ensemble algorithms for baseline model performance
  4. Explore algorithm tuning techniques for improving model performance

Any predictive modeling machine learning project genrally can be broken down into about six major tasks:

  1. Prepare Problem
  2. Summarize Data
  3. Prepare Data
  4. Model and Evaluate Algorithms
  5. Improve Accuracy or Results
  6. Finalize Model and Present Results

1. Prepare Problem

1.a) Load libraries

startTimeScript <- proc.time()
library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
library(corrplot)
## corrplot 0.84 loaded
library(mailR)
library(stringr)
library(MLmetrics)
## 
## Attaching package: 'MLmetrics'
## The following objects are masked from 'package:caret':
## 
##     MAE, RMSE
## The following object is masked from 'package:base':
## 
##     Recall
library(DMwR)
## Loading required package: grid
library(mlbench)

# Create one random seed number for reproducible results
seedNum <- 888
set.seed(seedNum)

1.b) Set up the email notification function

email_notify <- function(msg=""){
  sender <- "luozhi2488@gmail.com"
  receiver <- "dave@contactdavidlowe.com"
  sbj_line <- "Notification from R Multi-Class Classification Script"
  password <- readLines("../email_credential.txt")
  send.mail(
    from = sender,
    to = receiver,
    subject= sbj_line,
    body = msg,
    smtp = list(host.name = "smtp.gmail.com", port = 465, user.name = sender, passwd = password, ssl = TRUE),
    authenticate = TRUE,
    send = TRUE)
}
email_notify(paste("Library and Data Loading has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3c0f93f1}"

1.c) Load dataset

widthVector <- rep(16, 561)
colNames <- paste0("attr",1:561)
x_train <- read.csv("X_train.txt", header = FALSE, col.names = colNames, sep = " ")
y_train <- read.csv("Y_train.txt", header = FALSE, col.names = c("targetVar"))
y_train$targetVar <- as.factor(y_train$targetVar)
xy_train <- cbind(x_train, y_train)

x_test <- read.csv("X_test.txt", header = FALSE, col.names = colNames, sep = " ")
y_test <- read.csv("Y_test.txt", header = FALSE, col.names = c("targetVar"))
y_test$targetVar <- as.factor(y_test$targetVar)
xy_test <- cbind(x_test, y_test)
# Use variable totCol to hold the number of columns in the dataframe
totCol <- ncol(xy_train)

# Set up variable totAttr for the total number of attribute columns
totAttr <- totCol-1

1.d) Set up the key parameters to be used in the script

# Set up the number of row and columns for visualization display. dispRow * dispCol should be >= totAttr
dispCol <- 5
if (totAttr%%dispCol == 0) {
dispRow <- totAttr%/%dispCol
} else {
dispRow <- (totAttr%/%dispCol) + 1
}
cat("Will attempt to create graphics grid (col x row): ", dispCol, ' by ', dispRow)
## Will attempt to create graphics grid (col x row):  5  by  113

1.e) Set test options and evaluation metric

# Run algorithms using 10-fold cross validation
control <- trainControl(method="repeatedcv", number=10, repeats=1)
metricTarget <- "Accuracy"
email_notify(paste("Library and Data Loading completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@a67c67e}"

2. Summarize Data

To gain a better understanding of the data that we have on-hand, we will leverage a number of descriptive statistics and data visualization techniques. The plan is to use the results to consider new questions, review assumptions, and validate hypotheses that we can investigate later with specialized models.

email_notify(paste("Data Summarization and Visualization has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6fc6f14e}"

2.a) Descriptive statistics

2.a.i) Peek at the data itself.

head(xy_train)
##        attr1        attr2       attr3      attr4      attr5      attr6
## 1 0.04357967 -0.005970221 -0.03505434 -0.9953812 -0.9883659 -0.9373820
## 2 0.03948004 -0.002131276 -0.02906736 -0.9983480 -0.9829449 -0.9712729
## 3 0.03997778 -0.005152716 -0.02265071 -0.9954821 -0.9773138 -0.9847595
## 4 0.03978456 -0.011808778 -0.02891578 -0.9961941 -0.9885686 -0.9932556
## 5 0.03875814 -0.002288533 -0.02386289 -0.9982413 -0.9867741 -0.9931155
## 6 0.03898801  0.004108852 -0.01734026 -0.9974376 -0.9934854 -0.9966920
##        attr7      attr8      attr9     attr10     attr11     attr12
## 1 -0.9950070 -0.9888156 -0.9533252 -0.7947964 -0.7448928 -0.6484472
## 2 -0.9987020 -0.9833148 -0.9739998 -0.8025366 -0.7363378 -0.7124148
## 3 -0.9964148 -0.9758348 -0.9859730 -0.7984772 -0.7363378 -0.7124148
## 4 -0.9969943 -0.9885264 -0.9931354 -0.7984772 -0.7527779 -0.7221857
## 5 -0.9982159 -0.9864792 -0.9938246 -0.8019815 -0.7465054 -0.7178581
## 6 -0.9975222 -0.9934935 -0.9969160 -0.8019815 -0.7433715 -0.7161817
##      attr13    attr14    attr15     attr16     attr17     attr18
## 1 0.8417956 0.7084402 0.6517165 -0.9757520 -0.9999502 -0.9998884
## 2 0.8387581 0.7084402 0.6593403 -0.9874270 -0.9999927 -0.9998263
## 3 0.8340019 0.7050081 0.6745507 -0.9885282 -0.9999725 -0.9997194
## 4 0.8340019 0.7050081 0.6732080 -0.9903894 -0.9999784 -0.9997827
## 5 0.8385806 0.7058541 0.6732080 -0.9950571 -0.9999921 -0.9998824
## 6 0.8385806 0.7181487 0.6805388 -0.9959641 -0.9999874 -0.9998833
##       attr19     attr20     attr21     attr22     attr23     attr24
## 1 -0.9980137 -0.9939993 -0.9919796 -0.9709701 -0.5470954 -0.7009736
## 2 -0.9994107 -0.9989183 -0.9854825 -0.9734814 -0.7819734 -0.5346039
## 3 -0.9998026 -0.9968982 -0.9767812 -0.9867541 -0.6881761 -0.5205140
## 4 -0.9998152 -0.9969486 -0.9894371 -0.9924404 -0.7151026 -0.8609883
## 5 -0.9999083 -0.9977723 -0.9877261 -0.9951089 -0.8367735 -0.5892004
## 6 -0.9999675 -0.9973519 -0.9948008 -0.9971607 -0.8102506 -0.4915608
##       attr25    attr26      attr27    attr28      attr29     attr30
## 1 -0.6226971 0.9218842 -0.71948288 0.3421680 -0.16131765 0.26604897
## 2 -0.5931648 0.6074353 -0.26678274 0.2758824  0.20041658 0.13126564
## 3 -0.5931648 0.2722625 -0.05642431 0.3222829 -0.27329167 0.03717982
## 4 -0.9164289 0.0628164  0.08293970 0.2005662 -0.37826161 0.09006277
## 5 -0.7737707 0.3121055 -0.09525383 0.1943987 -0.00799849 0.26673995
## 6 -0.5741065 0.3881044 -0.13941549 0.1660186  0.09785734 0.26896972
##       attr31    attr32      attr33    attr34      attr35     attr36
## 1 -0.2743515 0.2672051 -0.02095843 0.3826102 -0.50174806 0.51246321
## 2 -0.1490167 0.2924360 -0.19298551 0.2174964 -0.08917505 0.05990858
## 3 -0.1336120 0.3324868 -0.24049052 0.3487328 -0.19540881 0.22943640
## 4 -0.2092639 0.3165300 -0.09086207 0.3963826 -0.35364269 0.50375356
## 5 -0.3189649 0.4097313 -0.22458943 0.5203539 -0.31916749 0.23437579
## 6 -0.2915595 0.3988789 -0.31994831 0.6219899 -0.27191893 0.22167264
##        attr37      attr38      attr39    attr40    attr41     attr42
## 1 -0.20633687  0.37677800  0.43517232 0.6601985 0.9600507 -0.1359387
## 2 -0.23660913 -0.01269628 -0.07271079 0.5786491 0.9632148 -0.1366480
## 3 -0.31681581 -0.12388942 -0.18113694 0.6082186 0.9635317 -0.1371051
## 4 -0.49038926 -0.30475944 -0.36270837 0.5066018 0.9642686 -0.1390654
## 5 -0.10265050 -0.15497394 -0.18979591 0.5985146 0.9648776 -0.1438237
## 6  0.07014599 -0.20911148 -0.15109212 0.1790016 0.9646015 -0.1432852
##       attr43     attr44     attr45     attr46     attr47     attr48
## 1 0.11555554 -0.9881345 -0.9826928 -0.9197227 -0.9883619 -0.9855230
## 2 0.10955844 -0.9979176 -0.9900056 -0.9551601 -0.9983578 -0.9903461
## 3 0.10206233 -0.9996573 -0.9932357 -0.9953640 -0.9997170 -0.9931219
## 4 0.10002822 -0.9973016 -0.9823946 -0.9858896 -0.9972507 -0.9823173
## 5 0.09466311 -0.9987365 -0.9887307 -0.9860658 -0.9987672 -0.9894554
## 6 0.09208651 -0.9991789 -0.9874604 -0.9982436 -0.9992659 -0.9875346
##       attr49    attr50     attr51     attr52    attr53     attr54
## 1 -0.9318338 0.8920545 -0.1613504 0.12465977 0.9774363 -0.1215128
## 2 -0.9567964 0.8920603 -0.1614275 0.12258573 0.9845201 -0.1132053
## 3 -0.9954374 0.8924006 -0.1637959 0.09456584 0.9867701 -0.1132053
## 4 -0.9860652 0.8938171 -0.1637959 0.09342467 0.9868211 -0.1196380
## 5 -0.9863758 0.8938171 -0.1668706 0.09168239 0.9874335 -0.1201351
## 6 -0.9983404 0.8936834 -0.1670548 0.08334712 0.9877218 -0.1201351
##       attr55     attr56    attr57     attr58     attr59     attr60
## 1 0.05611428 -0.3744642 0.8918215 -0.9708356 -0.9755107 -0.9891408
## 2 0.10237952 -0.3824801 0.9001481 -0.9705123 -0.9785008 -0.9994364
## 3 0.10237952 -0.4006802 0.9009836 -0.9702972 -0.9816727 -0.9997762
## 4 0.09537050 -0.3993546 0.9029287 -0.9693264 -0.9824200 -0.9972114
## 5 0.09367780 -0.3995534 0.9045361 -0.9669723 -0.9843630 -0.9988336
## 6 0.09367780 -0.4084490 0.9038070 -0.9672424 -0.9852757 -0.9995472
##       attr61     attr62 attr63 attr64      attr65       attr66     attr67
## 1 -0.9904443 -0.9488870     -1     -1  0.03424856 -0.593146212 0.59463587
## 2 -0.9914546 -0.9637786     -1     -1 -0.26688692 -0.414654102 0.41970738
## 3 -0.9932328 -0.9954574     -1     -1 -0.93200653 -0.006655758 0.03847818
## 4 -0.9834323 -0.9874714     -1     -1 -0.62495078 -0.073125639 0.08578606
## 5 -0.9919538 -0.9878656     -1     -1 -0.64396547 -0.263455687 0.27669978
## 6 -0.9884875 -0.9986352     -1     -1 -1.00000000 -0.307945770 0.38534698
##        attr68    attr69      attr70     attr71      attr72     attr73
## 1 -0.59643990 0.5985603 -0.71220910 0.70963040 -0.70748448 0.70500050
## 2 -0.42506575 0.4307221 -0.09034915 0.08933676 -0.08980775 0.09027531
## 3 -0.07009309 0.1014171 -0.24059474 0.24053159 -0.24139845 0.24186914
## 4 -0.09871488 0.1118854 -0.20210338 0.19658572 -0.19232572 0.18797520
## 5 -0.29038937 0.3044995 -0.05675133 0.05246193 -0.04986365 0.04744427
## 6 -0.46407635 0.5439649 -0.09234864 0.09125391 -0.09182956 0.09259692
##       attr74    attr75     attr76    attr77     attr78     attr79
## 1 -0.9921171 0.9926469 -0.9928854 0.9917479  0.5702688  0.4390651
## 2 -0.8329200 0.8332964 -0.8334545 0.8323968 -0.8312777 -0.8655856
## 3 -0.7057012 0.7149424 -0.7239782 0.7318479 -0.1810648  0.3379804
## 4 -0.3901013 0.3910961 -0.3920717 0.3922717 -0.9913072 -0.9686889
## 5 -0.2440304 0.2458628 -0.2478208 0.2492269 -0.4083119 -0.1847604
## 6 -0.1654648 0.1827825 -0.2001898 0.2169948 -0.5639370  0.4665066
##      attr80     attr81      attr82      attr83     attr84     attr85
## 1 0.9869130 0.07799634 0.005000803 -0.09778959 -0.9935191 -0.9883600
## 2 0.9743853 0.07400671 0.005771104 -0.01217132 -0.9955481 -0.9810636
## 3 0.6434127 0.07363596 0.003104037 -0.04601284 -0.9907428 -0.9809556
## 4 0.9842553 0.07732061 0.020057642 -0.04673432 -0.9926974 -0.9875528
## 5 0.9647961 0.07344436 0.019121574 -0.02326619 -0.9964202 -0.9883587
## 6 0.4430904 0.07793244 0.018684046 -0.02981526 -0.9948136 -0.9887145
##       attr86     attr87     attr88     attr89     attr90     attr91
## 1 -0.9935750 -0.9944374 -0.9862066 -0.9928184 -0.9851801 -0.9919942
## 2 -0.9918457 -0.9955817 -0.9789380 -0.9912766 -0.9945447 -0.9790682
## 3 -0.9896866 -0.9908828 -0.9793002 -0.9872381 -0.9870770 -0.9790682
## 4 -0.9934976 -0.9942157 -0.9857170 -0.9914832 -0.9870770 -0.9917862
## 5 -0.9924549 -0.9965471 -0.9865370 -0.9906864 -0.9969933 -0.9918178
## 6 -0.9922663 -0.9951916 -0.9868467 -0.9910667 -0.9941054 -0.9918178
##       attr92    attr93    attr94    attr95     attr96     attr97
## 1 -0.9931189 0.9898347 0.9919569 0.9905192 -0.9936582 -0.9999349
## 2 -0.9922574 0.9925771 0.9918084 0.9885391 -0.9915297 -0.9999597
## 3 -0.9922574 0.9883902 0.9918084 0.9885391 -0.9882835 -0.9998942
## 4 -0.9897689 0.9883902 0.9925438 0.9932176 -0.9930045 -0.9999236
## 5 -0.9897689 0.9943032 0.9925438 0.9856091 -0.9939682 -0.9999692
## 6 -0.9926493 0.9943032 0.9933463 0.9856091 -0.9936092 -0.9999512
##       attr98     attr99    attr100    attr101    attr102    attr103
## 1 -0.9998204 -0.9998785 -0.9944068 -0.9860249 -0.9886976 -0.8199493
## 2 -0.9996396 -0.9998454 -0.9939055 -0.9794351 -0.9928467 -0.8750964
## 3 -0.9996364 -0.9997950 -0.9878883 -0.9801445 -0.9813768 -0.7536287
## 4 -0.9998029 -0.9998829 -0.9947207 -0.9870330 -0.9883604 -0.8208042
## 5 -0.9998203 -0.9998599 -0.9959306 -0.9865242 -0.9900354 -0.8507439
## 6 -0.9998278 -0.9998560 -0.9953237 -0.9873590 -0.9890159 -0.7787178
##      attr104    attr105   attr106      attr107   attr108   attr109
## 1 -0.7930464 -0.8631452 0.9480263 -0.334807052 0.7142020 0.4986861
## 2 -0.6553621 -0.7433264 0.4787576 -0.056439286 0.4697268 0.6490987
## 3 -0.6732736 -0.7233282 0.2723818  0.055575744 0.5605804 0.4815343
## 4 -0.7549682 -0.8004361 0.1415040  0.139563948 0.5542138 0.2895027
## 5 -0.7462578 -0.7725026 0.2500183  0.004544708 0.4110317 0.3904927
## 6 -0.7549682 -0.7665115 0.2865986 -0.028337038 0.3778878 0.2986920
##     attr110     attr111   attr112   attr113   attr114      attr115
## 1 0.2966808 -0.18951272 0.3109116 0.2371101 0.4109366 -0.509475111
## 2 0.2140384 -0.08939874 0.3969624 0.2808034 0.2165530  0.112392130
## 3 0.1540988 -0.14811116 0.3621401 0.3070301 0.3366697  0.020750601
## 4 0.1718296 -0.23023560 0.2546607 0.3578172 0.4249952 -0.192279269
## 5 0.3663556 -0.26870767 0.4835351 0.2856164 0.4532194 -0.062401073
## 6 0.3947460 -0.21125744 0.5525029 0.2137284 0.4347620 -0.001329791
##     attr116    attr117    attr118      attr119     attr120      attr121
## 1 0.4755736 -0.3522074 -0.3946309 -0.016790470 -0.15823668 -0.006100849
## 2 0.2554888  0.2017795 -0.2169136  0.032498466 -0.29512064 -0.016111620
## 3 0.3963886  0.2707450 -0.1276489 -0.157126194 -0.07482247 -0.031698294
## 4 0.5085598  0.4470294 -0.1350891 -0.130999590  0.40413819 -0.043409983
## 5 0.3724474  0.2134843 -0.2814568  0.051019425  0.02605744 -0.033960416
## 6 0.3563432  0.3157658 -0.3838693 -0.008798576 -0.14404291 -0.028775508
##        attr122     attr123    attr124    attr125    attr126    attr127
## 1  0.007514728 -0.06386164 -0.9853121 -0.9766076 -0.9933188 -0.9845891
## 2 -0.027651251 -0.06848507 -0.9831218 -0.9890298 -0.9907206 -0.9868933
## 3 -0.039997164 -0.07137096 -0.9762939 -0.9935358 -0.9884102 -0.9749244
## 4 -0.032667105 -0.07822679 -0.9913866 -0.9923913 -0.9894005 -0.9915918
## 5 -0.021501776 -0.08350060 -0.9851854 -0.9923621 -0.9892721 -0.9869466
## 6 -0.018613112 -0.08245169 -0.9851826 -0.9921015 -0.9856284 -0.9857885
##      attr128    attr129    attr130    attr131    attr132   attr133
## 1 -0.9763265 -0.9933414 -0.8975631 -0.9366760 -0.7626443 0.8542972
## 2 -0.9890117 -0.9906226 -0.8960751 -0.9564800 -0.7610341 0.8406589
## 3 -0.9940957 -0.9877144 -0.8960751 -0.9619768 -0.7585727 0.8406589
## 4 -0.9931157 -0.9909652 -0.9102716 -0.9595805 -0.7585727 0.8411034
## 5 -0.9925161 -0.9897482 -0.8997258 -0.9562789 -0.7647459 0.8460487
## 6 -0.9922423 -0.9850775 -0.8997258 -0.9562789 -0.7615367 0.8467689
##     attr134   attr135    attr136    attr137    attr138    attr139
## 1 0.8950316 0.8308405 -0.9671216 -0.9995782 -0.9993543 -0.9998181
## 2 0.8883163 0.8289350 -0.9805500 -0.9997557 -0.9998973 -0.9998634
## 3 0.8859839 0.8289350 -0.9762173 -0.9996933 -0.9998283 -0.9998627
## 4 0.8859839 0.8266338 -0.9822325 -0.9997928 -0.9999023 -0.9999055
## 5 0.8913592 0.8213744 -0.9851988 -0.9998494 -0.9999519 -0.9998802
## 6 0.8913592 0.8188267 -0.9851510 -0.9998739 -0.9999466 -0.9998293
##      attr140    attr141    attr142      attr143    attr144    attr145
## 1 -0.9843995 -0.9785768 -0.9930527  0.082631682  0.1745154 -0.2184370
## 2 -0.9932488 -0.9893073 -0.9903272  0.007469356 -0.5419790 -0.2266056
## 3 -0.9739585 -0.9951068 -0.9869179 -0.260942672 -1.0000000 -0.2932927
## 4 -0.9915519 -0.9941278 -0.9946692 -0.930551143 -0.8306202 -0.5707097
## 5 -0.9904046 -0.9932992 -0.9912416 -0.628860991 -0.4800923 -0.6717193
## 6 -0.9861885 -0.9929566 -0.9837923 -0.363801069 -0.3850386 -0.4942727
##       attr146     attr147    attr148     attr149     attr150     attr151
## 1  0.32092613 -0.45260357 0.46613254 -0.20363231  1.00000000 -1.00000000
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## 5 -0.8571237 -0.9914330 -0.9890506 -0.9879320 -0.9921451 -0.9984044
## 6 -0.8007715 -0.9905000 -0.9858522 -0.9857459 -0.9891423 -0.9949489
##      attr534    attr535    attr536    attr537    attr538     attr539
## 1 -0.9801349 -0.9992404 -0.9926734 -0.7012914 -1.0000000 -0.13248000
## 2 -0.9882956 -0.9998112 -0.9939964 -0.7206830 -0.9487179 -0.26897852
## 3 -0.9892548 -0.9998539 -0.9932562 -0.7365215 -0.7948718 -0.21242883
## 4 -0.9894128 -0.9998756 -0.9891534 -0.7208908 -1.0000000 -0.04339843
## 5 -0.9914330 -0.9999018 -0.9893389 -0.7633721 -0.8974359 -0.27052857
## 6 -0.9905000 -0.9998606 -0.9919846 -0.7685767 -1.0000000 -0.29320080
##      attr540    attr541    attr542    attr543    attr544    attr545
## 1  0.5656971  0.3634775 -0.9919941 -0.9908772 -0.9901692 -0.9925210
## 2 -0.3642192 -0.7237243 -0.9958575 -0.9965797 -0.9956711 -0.9969393
## 3 -0.5648683 -0.8745940 -0.9950341 -0.9953075 -0.9948685 -0.9961329
## 4 -0.2571419 -0.5163411 -0.9952243 -0.9954170 -0.9959512 -0.9953464
## 5 -0.5395956 -0.8336609 -0.9950964 -0.9956450 -0.9955076 -0.9956826
## 6 -0.3740320 -0.7309306 -0.9951469 -0.9954188 -0.9946267 -0.9961612
##      attr546    attr547    attr548    attr549    attr550    attr551
## 1 -0.9910440 -0.9919941 -0.9999368 -0.9905369 -0.8713058 -1.0000000
## 2 -0.9944359 -0.9958575 -0.9999807 -0.9946229 -1.0000000 -1.0000000
## 3 -0.9958625 -0.9950341 -0.9999731 -0.9938344 -1.0000000 -0.5555556
## 4 -0.9957280 -0.9952243 -0.9999744 -0.9953052 -0.9556959 -0.9365079
## 5 -0.9974142 -0.9950964 -0.9999745 -0.9955660 -1.0000000 -0.9365079
## 6 -0.9985156 -0.9951469 -0.9999740 -0.9946096 -1.0000000 -1.0000000
##       attr552    attr553    attr554     attr555      attr556    attr557
## 1 -0.01223589 -0.3148484 -0.7133078 -0.11275434  0.030400372 -0.4647614
## 2  0.20280381 -0.6031992 -0.8606769  0.05347696 -0.007434566 -0.7326262
## 3  0.44007936 -0.4044275 -0.7618472 -0.11855926  0.177899475  0.1006992
## 4  0.43089077 -0.1383728 -0.4916043 -0.03678797 -0.012892494  0.6400110
## 5  0.13773462 -0.3662136 -0.7024898  0.12332005  0.122541962  0.6935783
## 6  0.07499891 -0.5549023 -0.8442241  0.08263216 -0.143439015  0.2750407
##       attr558    attr559   attr560     attr561 targetVar
## 1 -0.01844588 -0.8415585 0.1799128 -0.05171842         5
## 2  0.70351059 -0.8450924 0.1802611 -0.04743634         5
## 3  0.80852908 -0.8492301 0.1806096 -0.04227136         5
## 4 -0.48536645 -0.8489466 0.1819071 -0.04082622         5
## 5 -0.61597061 -0.8481640 0.1851237 -0.03707990         5
## 6 -0.36822404 -0.8499269 0.1847950 -0.03532556         5

2.a.ii) Dimensions of the dataset.

dim(xy_train)
## [1] 7767  562

2.a.iii) Types of the attributes.

sapply(xy_train, class)
##     attr1     attr2     attr3     attr4     attr5     attr6     attr7 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##     attr8     attr9    attr10    attr11    attr12    attr13    attr14 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr15    attr16    attr17    attr18    attr19    attr20    attr21 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr22    attr23    attr24    attr25    attr26    attr27    attr28 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr29    attr30    attr31    attr32    attr33    attr34    attr35 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr36    attr37    attr38    attr39    attr40    attr41    attr42 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr43    attr44    attr45    attr46    attr47    attr48    attr49 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr50    attr51    attr52    attr53    attr54    attr55    attr56 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr57    attr58    attr59    attr60    attr61    attr62    attr63 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr64    attr65    attr66    attr67    attr68    attr69    attr70 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr71    attr72    attr73    attr74    attr75    attr76    attr77 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr78    attr79    attr80    attr81    attr82    attr83    attr84 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr85    attr86    attr87    attr88    attr89    attr90    attr91 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr92    attr93    attr94    attr95    attr96    attr97    attr98 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr99   attr100   attr101   attr102   attr103   attr104   attr105 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr106   attr107   attr108   attr109   attr110   attr111   attr112 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr113   attr114   attr115   attr116   attr117   attr118   attr119 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr120   attr121   attr122   attr123   attr124   attr125   attr126 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr127   attr128   attr129   attr130   attr131   attr132   attr133 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr134   attr135   attr136   attr137   attr138   attr139   attr140 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr141   attr142   attr143   attr144   attr145   attr146   attr147 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr148   attr149   attr150   attr151   attr152   attr153   attr154 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr155   attr156   attr157   attr158   attr159   attr160   attr161 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr162   attr163   attr164   attr165   attr166   attr167   attr168 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr169   attr170   attr171   attr172   attr173   attr174   attr175 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr176   attr177   attr178   attr179   attr180   attr181   attr182 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr183   attr184   attr185   attr186   attr187   attr188   attr189 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr190   attr191   attr192   attr193   attr194   attr195   attr196 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr197   attr198   attr199   attr200   attr201   attr202   attr203 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr204   attr205   attr206   attr207   attr208   attr209   attr210 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr211   attr212   attr213   attr214   attr215   attr216   attr217 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr218   attr219   attr220   attr221   attr222   attr223   attr224 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr225   attr226   attr227   attr228   attr229   attr230   attr231 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr232   attr233   attr234   attr235   attr236   attr237   attr238 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr239   attr240   attr241   attr242   attr243   attr244   attr245 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr246   attr247   attr248   attr249   attr250   attr251   attr252 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr253   attr254   attr255   attr256   attr257   attr258   attr259 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr260   attr261   attr262   attr263   attr264   attr265   attr266 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr267   attr268   attr269   attr270   attr271   attr272   attr273 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr274   attr275   attr276   attr277   attr278   attr279   attr280 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr281   attr282   attr283   attr284   attr285   attr286   attr287 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr288   attr289   attr290   attr291   attr292   attr293   attr294 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr295   attr296   attr297   attr298   attr299   attr300   attr301 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr302   attr303   attr304   attr305   attr306   attr307   attr308 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr309   attr310   attr311   attr312   attr313   attr314   attr315 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr316   attr317   attr318   attr319   attr320   attr321   attr322 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr323   attr324   attr325   attr326   attr327   attr328   attr329 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr330   attr331   attr332   attr333   attr334   attr335   attr336 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr337   attr338   attr339   attr340   attr341   attr342   attr343 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr344   attr345   attr346   attr347   attr348   attr349   attr350 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr351   attr352   attr353   attr354   attr355   attr356   attr357 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr358   attr359   attr360   attr361   attr362   attr363   attr364 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr365   attr366   attr367   attr368   attr369   attr370   attr371 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr372   attr373   attr374   attr375   attr376   attr377   attr378 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr379   attr380   attr381   attr382   attr383   attr384   attr385 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr386   attr387   attr388   attr389   attr390   attr391   attr392 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr393   attr394   attr395   attr396   attr397   attr398   attr399 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr400   attr401   attr402   attr403   attr404   attr405   attr406 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr407   attr408   attr409   attr410   attr411   attr412   attr413 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr414   attr415   attr416   attr417   attr418   attr419   attr420 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr421   attr422   attr423   attr424   attr425   attr426   attr427 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr428   attr429   attr430   attr431   attr432   attr433   attr434 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr435   attr436   attr437   attr438   attr439   attr440   attr441 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr442   attr443   attr444   attr445   attr446   attr447   attr448 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr449   attr450   attr451   attr452   attr453   attr454   attr455 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr456   attr457   attr458   attr459   attr460   attr461   attr462 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr463   attr464   attr465   attr466   attr467   attr468   attr469 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr470   attr471   attr472   attr473   attr474   attr475   attr476 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr477   attr478   attr479   attr480   attr481   attr482   attr483 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr484   attr485   attr486   attr487   attr488   attr489   attr490 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr491   attr492   attr493   attr494   attr495   attr496   attr497 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr498   attr499   attr500   attr501   attr502   attr503   attr504 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr505   attr506   attr507   attr508   attr509   attr510   attr511 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr512   attr513   attr514   attr515   attr516   attr517   attr518 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr519   attr520   attr521   attr522   attr523   attr524   attr525 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr526   attr527   attr528   attr529   attr530   attr531   attr532 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr533   attr534   attr535   attr536   attr537   attr538   attr539 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr540   attr541   attr542   attr543   attr544   attr545   attr546 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr547   attr548   attr549   attr550   attr551   attr552   attr553 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr554   attr555   attr556   attr557   attr558   attr559   attr560 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr561 targetVar 
## "numeric"  "factor"

2.a.iv) Statistical summary of all attributes.

summary(xy_train)
##      attr1              attr2                attr3         
##  Min.   :-1.00000   Min.   :-1.0000000   Min.   :-1.00000  
##  1st Qu.: 0.03204   1st Qu.:-0.0112093   1st Qu.:-0.02845  
##  Median : 0.03897   Median :-0.0029213   Median :-0.01960  
##  Mean   : 0.03876   Mean   :-0.0006466   Mean   :-0.01815  
##  3rd Qu.: 0.04400   3rd Qu.: 0.0043027   3rd Qu.:-0.01168  
##  Max.   : 1.00000   Max.   : 1.0000000   Max.   : 1.00000  
##                                                            
##      attr4             attr5             attr6             attr7        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9921   1st Qu.:-0.9836   1st Qu.:-0.9847   1st Qu.:-0.9929  
##  Median :-0.9142   Median :-0.8280   Median :-0.8277   Median :-0.9244  
##  Mean   :-0.5990   Mean   :-0.6344   Mean   :-0.6913   Mean   :-0.6239  
##  3rd Qu.:-0.2460   3rd Qu.:-0.3131   3rd Qu.:-0.4505   3rd Qu.:-0.2949  
##  Max.   : 1.0000   Max.   : 0.9460   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr8             attr9             attr10             attr11       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.0000  
##  1st Qu.:-0.9841   1st Qu.:-0.9867   1st Qu.:-0.79561   1st Qu.:-0.7407  
##  Median :-0.8386   Median :-0.8527   Median :-0.71701   Median :-0.6224  
##  Mean   :-0.6579   Mean   :-0.7402   Mean   :-0.36020   Mean   :-0.4925  
##  3rd Qu.:-0.3627   3rd Qu.:-0.5405   3rd Qu.: 0.05418   3rd Qu.:-0.2847  
##  Max.   : 0.9603   Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.0000  
##                                                                          
##      attr12            attr13            attr14            attr15       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.7068   1st Qu.: 0.2923   1st Qu.: 0.1205   1st Qu.: 0.2613  
##  Median :-0.6090   Median : 0.7707   Median : 0.6136   Median : 0.5885  
##  Mean   :-0.4723   Mean   : 0.5593   Mean   : 0.4015   Mean   : 0.4432  
##  3rd Qu.:-0.2808   3rd Qu.: 0.8341   3rd Qu.: 0.7075   3rd Qu.: 0.6721  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr16            attr17            attr18            attr19       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9871   1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-0.9998  
##  Median :-0.8547   Median :-0.9949   Median :-0.9851   Median :-0.9851  
##  Mean   :-0.6491   Mean   :-0.8258   Mean   :-0.8950   Mean   :-0.9264  
##  3rd Qu.:-0.3457   3rd Qu.:-0.7263   3rd Qu.:-0.8375   3rd Qu.:-0.9006  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9779   Max.   : 1.0000  
##                                                                         
##      attr20            attr21            attr22            attr23        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.9938   1st Qu.:-0.9873   1st Qu.:-0.9886   1st Qu.:-0.67065  
##  Median :-0.9328   Median :-0.8839   Median :-0.8864   Median :-0.28099  
##  Mean   :-0.6770   Mean   :-0.7372   Mean   :-0.7940   Mean   :-0.29896  
##  3rd Qu.:-0.3909   3rd Qu.:-0.5248   3rd Qu.:-0.6426   3rd Qu.: 0.02878  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.00000  
##                                                                          
##      attr24            attr25            attr26            attr27        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.5863   1st Qu.:-0.5299   1st Qu.:-0.3692   1st Qu.:-0.04681  
##  Median :-0.1567   Median :-0.1781   Median :-0.1481   Median : 0.08796  
##  Mean   :-0.1815   Mean   :-0.1953   Mean   :-0.1255   Mean   : 0.11461  
##  3rd Qu.: 0.1993   3rd Qu.: 0.1124   3rd Qu.: 0.1228   3rd Qu.: 0.26730  
##  Max.   : 1.0000   Max.   : 0.9998   Max.   : 1.0000   Max.   : 1.00000  
##                                                                          
##      attr28              attr29             attr30        
##  Min.   :-1.000000   Min.   :-0.93037   Min.   :-1.00000  
##  1st Qu.:-0.152010   1st Qu.:-0.12769   1st Qu.:-0.20740  
##  Median : 0.003232   Median : 0.04035   Median :-0.03653  
##  Mean   :-0.013326   Mean   : 0.03539   Mean   :-0.01856  
##  3rd Qu.: 0.136935   3rd Qu.: 0.19850   3rd Qu.: 0.17333  
##  Max.   : 1.000000   Max.   : 1.00000   Max.   : 1.00000  
##                                                           
##      attr31             attr32             attr33        
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-0.90971  
##  1st Qu.:-0.18465   1st Qu.: 0.06698   1st Qu.:-0.09028  
##  Median :-0.04382   Median : 0.18080   Median : 0.04813  
##  Mean   :-0.03071   Mean   : 0.17369   Mean   : 0.04787  
##  3rd Qu.: 0.11213   3rd Qu.: 0.28884   3rd Qu.: 0.18709  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 0.99290  
##                                                          
##      attr34             attr35             attr36        
##  Min.   :-1.00000   Min.   :-0.97693   Min.   :-1.00000  
##  1st Qu.:-0.05212   1st Qu.:-0.17760   1st Qu.:-0.03675  
##  Median : 0.15061   Median :-0.05570   Median : 0.10904  
##  Mean   : 0.13832   Mean   :-0.03068   Mean   : 0.09661  
##  3rd Qu.: 0.33184   3rd Qu.: 0.10365   3rd Qu.: 0.24399  
##  Max.   : 0.91541   Max.   : 1.00000   Max.   : 0.96924  
##                                                          
##      attr37             attr38             attr39         
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.000000  
##  1st Qu.:-0.24979   1st Qu.:-0.38748   1st Qu.:-0.412106  
##  Median :-0.08732   Median :-0.16776   Median :-0.192983  
##  Mean   :-0.08308   Mean   :-0.13143   Mean   :-0.195810  
##  3rd Qu.: 0.07848   3rd Qu.: 0.07219   3rd Qu.: 0.007006  
##  Max.   : 0.88413   Max.   : 1.00000   Max.   : 1.000000  
##                                                           
##      attr40            attr41            attr42             attr43        
##  Min.   :-0.9825   Min.   :-1.0000   Min.   :-0.53822   Min.   :-1.00000  
##  1st Qu.:-0.1564   1st Qu.: 0.7761   1st Qu.:-0.23172   1st Qu.:-0.11782  
##  Median : 0.1480   Median : 0.9126   Median :-0.13117   Median : 0.03384  
##  Mean   : 0.1064   Mean   : 0.6552   Mean   : 0.02554   Mean   : 0.09809  
##  3rd Qu.: 0.3892   3rd Qu.: 0.9484   3rd Qu.: 0.19152   3rd Qu.: 0.23909  
##  Max.   : 1.0000   Max.   : 0.9847   Max.   : 1.00000   Max.   : 1.00000  
##                                                                           
##      attr44            attr45            attr46            attr47       
##  Min.   :-1.0000   Min.   :-0.9999   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9956   1st Qu.:-0.9914   1st Qu.:-0.9908   1st Qu.:-0.9958  
##  Median :-0.9841   Median :-0.9753   Median :-0.9758   Median :-0.9853  
##  Mean   :-0.9436   Mean   :-0.9261   Mean   :-0.9368   Mean   :-0.9467  
##  3rd Qu.:-0.9641   3rd Qu.:-0.9433   3rd Qu.:-0.9456   3rd Qu.:-0.9663  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr48            attr49            attr50            attr51        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.49393  
##  1st Qu.:-0.9917   1st Qu.:-0.9911   1st Qu.: 0.7432   1st Qu.:-0.24294  
##  Median :-0.9767   Median :-0.9770   Median : 0.8569   Median :-0.14457  
##  Mean   :-0.9288   Mean   :-0.9389   Mean   : 0.6111   Mean   : 0.01543  
##  3rd Qu.:-0.9458   3rd Qu.:-0.9478   3rd Qu.: 0.8867   3rd Qu.: 0.19408  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.96811  
##                                                                          
##      attr52             attr53            attr54        
##  Min.   :-1.00000   Min.   :-1.0000   Min.   :-0.64863  
##  1st Qu.:-0.11005   1st Qu.: 0.7680   1st Qu.:-0.22357  
##  Median : 0.04789   Median : 0.9236   Median :-0.12500  
##  Mean   : 0.11048   Mean   : 0.6613   Mean   : 0.02503  
##  3rd Qu.: 0.25594   3rd Qu.: 0.9628   3rd Qu.: 0.16822  
##  Max.   : 0.99659   Max.   : 1.0000   Max.   : 1.00000  
##                                                         
##      attr55             attr56             attr57            attr58       
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.14525   1st Qu.:-0.39233   1st Qu.: 0.4390   1st Qu.:-0.9654  
##  Median : 0.01094   Median :-0.10281   Median : 0.7693   Median :-0.9073  
##  Mean   : 0.07602   Mean   :-0.07242   Mean   : 0.4182   Mean   :-0.7216  
##  3rd Qu.: 0.21594   3rd Qu.: 0.23295   3rd Qu.: 0.8615   3rd Qu.:-0.7560  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 0.9591   Max.   : 1.0000  
##                                                                           
##      attr59            attr60            attr61            attr62       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9892   1st Qu.:-0.9964   1st Qu.:-0.9931   1st Qu.:-0.9924  
##  Median :-0.9401   Median :-0.9883   Median :-0.9813   Median :-0.9806  
##  Mean   :-0.7438   Mean   :-0.9560   Mean   :-0.9393   Mean   :-0.9460  
##  3rd Qu.:-0.7337   3rd Qu.:-0.9722   3rd Qu.:-0.9548   3rd Qu.:-0.9548  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9348   Max.   : 1.0000  
##                                                                         
##      attr63            attr64            attr65            attr66       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-0.6799  
##  Median :-0.7357   Median :-1.0000   Median :-0.8269   Median :-0.5386  
##  Mean   :-0.6471   Mean   :-0.8232   Mean   :-0.6684   Mean   :-0.5355  
##  3rd Qu.:-0.3915   3rd Qu.:-0.7794   3rd Qu.:-0.4215   3rd Qu.:-0.3900  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr67            attr68            attr69            attr70       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.: 0.4285   1st Qu.:-0.7645   1st Qu.: 0.4967   1st Qu.:-0.5266  
##  Median : 0.5824   Median :-0.6286   Median : 0.6714   Median :-0.2788  
##  Mean   : 0.5719   Mean   :-0.6078   Mean   : 0.6432   Mean   :-0.2869  
##  3rd Qu.: 0.7219   3rd Qu.:-0.4640   3rd Qu.: 0.8079   3rd Qu.:-0.0497  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr71            attr72            attr73            attr74       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.: 0.1060   1st Qu.:-0.5845   1st Qu.: 0.2233   1st Qu.:-0.6586  
##  Median : 0.3211   Median :-0.3723   Median : 0.4275   Median :-0.4553  
##  Mean   : 0.3293   Mean   :-0.3729   Mean   : 0.4164   Mean   :-0.4589  
##  3rd Qu.: 0.5519   3rd Qu.:-0.1700   3rd Qu.: 0.6245   3rd Qu.:-0.2660  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9996   Max.   : 0.6314  
##                                                                         
##      attr75            attr76            attr77            attr78       
##  Min.   :-0.6001   Min.   :-1.0000   Min.   :-0.5353   Min.   :-1.0000  
##  1st Qu.: 0.2956   1st Qu.:-0.6996   1st Qu.: 0.3486   1st Qu.:-0.5585  
##  Median : 0.4794   Median :-0.5032   Median : 0.5310   Median : 0.3588  
##  Mean   : 0.4828   Mean   :-0.5064   Mean   : 0.5287   Mean   : 0.1573  
##  3rd Qu.: 0.6788   3rd Qu.:-0.3234   3rd Qu.: 0.7218   3rd Qu.: 0.8385  
##  Max.   : 1.0000   Max.   : 0.5679   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr79            attr80            attr81        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.8244   1st Qu.:-0.5955   1st Qu.: 0.05899  
##  Median :-0.2402   Median : 0.2198   Median : 0.07592  
##  Mean   :-0.1133   Mean   : 0.1043   Mean   : 0.07747  
##  3rd Qu.: 0.6091   3rd Qu.: 0.8064   3rd Qu.: 0.09542  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.00000  
##                                                        
##      attr82              attr83             attr84       
##  Min.   :-1.000000   Min.   :-0.91882   Min.   :-1.0000  
##  1st Qu.:-0.022742   1st Qu.:-0.06928   1st Qu.:-0.9913  
##  Median : 0.010691   Median :-0.03903   Median :-0.9379  
##  Mean   : 0.006721   Mean   :-0.04034   Mean   :-0.6495  
##  3rd Qu.: 0.036395   3rd Qu.:-0.01158   3rd Qu.:-0.3087  
##  Max.   : 1.000000   Max.   : 0.91283   Max.   : 1.0000  
##                                                          
##      attr85            attr86            attr87            attr88       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9854   1st Qu.:-0.9892   1st Qu.:-0.9913   1st Qu.:-0.9837  
##  Median :-0.9031   Median :-0.9394   Median :-0.9459   Median :-0.9084  
##  Mean   :-0.6120   Mean   :-0.7619   Mean   :-0.6467   Mean   :-0.5970  
##  3rd Qu.:-0.2388   3rd Qu.:-0.5587   3rd Qu.:-0.2987   3rd Qu.:-0.2009  
##  Max.   : 0.8071   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##      attr89            attr90            attr91            attr92       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9879   1st Qu.:-0.9918   1st Qu.:-0.9902   1st Qu.:-0.9897  
##  Median :-0.9421   Median :-0.9263   Median :-0.9231   Median :-0.9409  
##  Mean   :-0.7559   Mean   :-0.7032   Mean   :-0.7503   Mean   :-0.8184  
##  3rd Qu.:-0.5467   3rd Qu.:-0.4770   3rd Qu.:-0.5403   3rd Qu.:-0.6886  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6244   Max.   : 1.0000  
##                                                                         
##      attr93            attr94            attr95            attr96       
##  Min.   :-1.0000   Min.   :-0.7469   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.: 0.2722   1st Qu.: 0.4203   1st Qu.: 0.5412   1st Qu.:-0.9900  
##  Median : 0.9187   Median : 0.9105   Median : 0.9225   Median :-0.9329  
##  Mean   : 0.6285   Mean   : 0.6889   Mean   : 0.7382   Mean   :-0.6519  
##  3rd Qu.: 0.9897   3rd Qu.: 0.9888   3rd Qu.: 0.9866   3rd Qu.:-0.2986  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9993   Max.   : 1.0000  
##                                                                         
##      attr97            attr98            attr99           attr100       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9900  
##  Median :-0.9977   Median :-0.9944   Median :-0.9973   Median :-0.9530  
##  Mean   :-0.8563   Mean   :-0.8327   Mean   :-0.9296   Mean   :-0.6366  
##  3rd Qu.:-0.7583   3rd Qu.:-0.7057   3rd Qu.:-0.8975   3rd Qu.:-0.2845  
##  Max.   : 1.0000   Max.   : 0.6344   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr101           attr102           attr103            attr104        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.9839   1st Qu.:-0.9858   1st Qu.:-0.73089   1st Qu.:-0.72998  
##  Median :-0.9325   Median :-0.9476   Median :-0.25949   Median :-0.21553  
##  Mean   :-0.6596   Mean   :-0.7699   Mean   :-0.08536   Mean   :-0.08115  
##  3rd Qu.:-0.3325   3rd Qu.:-0.5874   3rd Qu.: 0.57841   3rd Qu.: 0.56261  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.00000  
##                                                                           
##     attr105           attr106            attr107        
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.6977   1st Qu.:-0.30168   1st Qu.:-0.08445  
##  Median :-0.2925   Median :-0.08559   Median : 0.03561  
##  Mean   :-0.1039   Mean   :-0.07669   Mean   : 0.03416  
##  3rd Qu.: 0.4949   3rd Qu.: 0.15123   3rd Qu.: 0.15195  
##  Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.00000  
##                                                         
##     attr108            attr109            attr110         
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.000000  
##  1st Qu.: 0.05983   1st Qu.: 0.05888   1st Qu.:-0.177964  
##  Median : 0.20835   Median : 0.21036   Median :-0.004985  
##  Mean   : 0.19884   Mean   : 0.20278   Mean   : 0.008669  
##  3rd Qu.: 0.34921   3rd Qu.: 0.35734   3rd Qu.: 0.203625  
##  Max.   : 0.94451   Max.   : 1.00000   Max.   : 1.000000  
##                                                           
##     attr111            attr112           attr113        
##  Min.   :-0.96851   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.20318   1st Qu.: 0.1045   1st Qu.: 0.02307  
##  Median :-0.08796   Median : 0.2424   Median : 0.17725  
##  Mean   :-0.08602   Mean   : 0.2334   Mean   : 0.16785  
##  3rd Qu.: 0.03582   3rd Qu.: 0.3718   3rd Qu.: 0.32533  
##  Max.   : 1.00000   Max.   : 0.9273   Max.   : 1.00000  
##                                                         
##     attr114            attr115            attr116        
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-0.87812  
##  1st Qu.:-0.11162   1st Qu.:-0.07507   1st Qu.: 0.04303  
##  Median : 0.08606   Median : 0.03030   Median : 0.21046  
##  Mean   : 0.07209   Mean   : 0.03025   Mean   : 0.19363  
##  3rd Qu.: 0.26431   3rd Qu.: 0.13494   3rd Qu.: 0.36019  
##  Max.   : 1.00000   Max.   : 0.71771   Max.   : 1.00000  
##                                                          
##     attr117           attr118            attr119        
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.: 0.0303   1st Qu.:-0.32038   1st Qu.:-0.24147  
##  Median : 0.1799   Median :-0.15334   Median :-0.03919  
##  Mean   : 0.1661   Mean   :-0.15177   Mean   :-0.04239  
##  3rd Qu.: 0.3098   3rd Qu.: 0.01317   3rd Qu.: 0.15851  
##  Max.   : 1.0000   Max.   : 0.91014   Max.   : 1.00000  
##                                                         
##     attr120            attr121             attr122         
##  Min.   :-0.93231   Min.   :-0.914050   Min.   :-1.000000  
##  1st Qu.:-0.13298   1st Qu.:-0.047501   1st Qu.:-0.043021  
##  Median : 0.03930   Median :-0.027678   Median :-0.021450  
##  Mean   : 0.04614   Mean   :-0.028705   Mean   :-0.020532  
##  3rd Qu.: 0.22150   3rd Qu.:-0.006363   3rd Qu.:-0.002647  
##  Max.   : 0.92736   Max.   : 0.740403   Max.   : 0.742382  
##                                                            
##     attr123            attr124           attr125           attr126       
##  Min.   :-0.97271   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.9999  
##  1st Qu.:-0.09417   1st Qu.:-0.9870   1st Qu.:-0.9821   1st Qu.:-0.9876  
##  Median :-0.07785   Median :-0.8608   Median :-0.8798   Median :-0.8666  
##  Mean   :-0.07750   Mean   :-0.7083   Mean   :-0.6643   Mean   :-0.6888  
##  3rd Qu.:-0.06024   3rd Qu.:-0.4673   3rd Qu.:-0.4210   3rd Qu.:-0.4225  
##  Max.   : 0.92052   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6850  
##                                                                          
##     attr127           attr128           attr129           attr130       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.9998   Min.   :-1.0000  
##  1st Qu.:-0.9878   1st Qu.:-0.9833   1st Qu.:-0.9881   1st Qu.:-0.9051  
##  Median :-0.8711   Median :-0.8925   Median :-0.8694   Median :-0.8325  
##  Mean   :-0.7147   Mean   :-0.6770   Mean   :-0.6945   Mean   :-0.7345  
##  3rd Qu.:-0.4783   3rd Qu.:-0.4359   3rd Qu.:-0.4357   3rd Qu.:-0.5880  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.7117   Max.   : 0.7630  
##                                                                         
##     attr131           attr132           attr133           attr134       
##  Min.   :-1.0000   Min.   :-0.9514   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9505   1st Qu.:-0.7647   1st Qu.: 0.4628   1st Qu.: 0.5780  
##  Median :-0.8688   Median :-0.6316   Median : 0.7605   Median : 0.8120  
##  Mean   :-0.7302   Mean   :-0.5001   Mean   : 0.6325   Mean   : 0.7091  
##  3rd Qu.:-0.5695   3rd Qu.:-0.2812   3rd Qu.: 0.8449   3rd Qu.: 0.8864  
##  Max.   : 1.0000   Max.   : 0.9216   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr135           attr136           attr137           attr138       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.: 0.3015   1st Qu.:-0.9787   1st Qu.:-0.9999   1st Qu.:-0.9997  
##  Median : 0.7155   Median :-0.7503   Median :-0.9806   Median :-0.9858  
##  Mean   : 0.5481   Mean   :-0.5784   Mean   :-0.8948   Mean   :-0.8725  
##  3rd Qu.: 0.8232   3rd Qu.:-0.2139   3rd Qu.:-0.8271   3rd Qu.:-0.8260  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr139           attr140           attr141           attr142       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.9999  
##  1st Qu.:-0.9998   1st Qu.:-0.9900   1st Qu.:-0.9860   1st Qu.:-0.9895  
##  Median :-0.9713   Median :-0.9007   Median :-0.9132   Median :-0.8731  
##  Mean   :-0.8857   Mean   :-0.7361   Mean   :-0.7024   Mean   :-0.6972  
##  3rd Qu.:-0.8226   3rd Qu.:-0.5197   3rd Qu.:-0.4825   3rd Qu.:-0.4512  
##  Max.   : 0.5651   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr143           attr144            attr145        
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.5108   1st Qu.:-0.37540   1st Qu.:-0.50666  
##  Median :-0.1698   Median :-0.08972   Median :-0.03049  
##  Mean   :-0.1381   Mean   :-0.11729   Mean   :-0.11798  
##  3rd Qu.: 0.2035   3rd Qu.: 0.15914   3rd Qu.: 0.23382  
##  Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.00000  
##                                                         
##     attr146            attr147            attr148        
##  Min.   :-1.00000   Min.   :-0.95095   Min.   :-1.00000  
##  1st Qu.:-0.11019   1st Qu.:-0.24944   1st Qu.: 0.02781  
##  Median : 0.04031   Median :-0.11941   Median : 0.16537  
##  Mean   : 0.05686   Mean   :-0.11252   Mean   : 0.14971  
##  3rd Qu.: 0.22126   3rd Qu.: 0.01594   3rd Qu.: 0.28601  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 1.00000  
##                                                          
##     attr149            attr150            attr151        
##  Min.   :-0.87366   Min.   :-0.97859   Min.   :-1.00000  
##  1st Qu.:-0.22808   1st Qu.:-0.34828   1st Qu.: 0.02002  
##  Median :-0.06412   Median :-0.20481   Median : 0.15360  
##  Mean   :-0.06574   Mean   :-0.20113   Mean   : 0.15940  
##  3rd Qu.: 0.09289   3rd Qu.:-0.05621   3rd Qu.: 0.29605  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 0.97233  
##                                                          
##     attr152             attr153            attr154        
##  Min.   :-0.921682   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.161017   1st Qu.: 0.05361   1st Qu.:-0.29419  
##  Median :-0.005872   Median : 0.20463   Median :-0.07768  
##  Mean   :-0.011001   Mean   : 0.20392   Mean   :-0.04654  
##  3rd Qu.: 0.148418   3rd Qu.: 0.35703   3rd Qu.: 0.20841  
##  Max.   : 1.000000   Max.   : 1.00000   Max.   : 0.89737  
##                                                           
##     attr155            attr156            attr157        
##  Min.   :-0.95345   Min.   :-0.92990   Min.   :-1.00000  
##  1st Qu.:-0.21150   1st Qu.:-0.13051   1st Qu.:-0.10770  
##  Median : 0.03106   Median : 0.06815   Median : 0.06692  
##  Mean   : 0.02233   Mean   : 0.05014   Mean   : 0.06697  
##  3rd Qu.: 0.24091   3rd Qu.: 0.23811   3rd Qu.: 0.23808  
##  Max.   : 0.99200   Max.   : 1.00000   Max.   : 0.99474  
##                                                          
##     attr158           attr159              attr160       
##  Min.   :-1.0000   Min.   :-1.0000000   Min.   :-1.0000  
##  1st Qu.:-0.4492   1st Qu.:-0.2569799   1st Qu.:-0.4451  
##  Median :-0.1819   Median :-0.0201672   Median :-0.1153  
##  Mean   :-0.1622   Mean   :-0.0002321   Mean   :-0.1187  
##  3rd Qu.: 0.1057   3rd Qu.: 0.2540334   3rd Qu.: 0.1922  
##  Max.   : 1.0000   Max.   : 1.0000000   Max.   : 1.0000  
##                                                          
##     attr161            attr162            attr163        
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.11960   1st Qu.:-0.06167   1st Qu.:-0.08327  
##  Median :-0.09822   Median :-0.04053   Median :-0.05455  
##  Mean   :-0.09782   Mean   :-0.04182   Mean   :-0.05446  
##  3rd Qu.:-0.07714   3rd Qu.:-0.02382   3rd Qu.:-0.02864  
##  Max.   : 1.00000   Max.   : 0.84803   Max.   : 1.00000  
##                                                          
##     attr164           attr165           attr166           attr167       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9905   1st Qu.:-0.9925   1st Qu.:-0.9933   1st Qu.:-0.9908  
##  Median :-0.9121   Median :-0.9416   Median :-0.9339   Median :-0.9243  
##  Mean   :-0.7303   Mean   :-0.7855   Mean   :-0.7440   Mean   :-0.7288  
##  3rd Qu.:-0.5004   3rd Qu.:-0.6428   3rd Qu.:-0.5204   3rd Qu.:-0.4879  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr168           attr169           attr170           attr171       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9930   1st Qu.:-0.9934   1st Qu.:-0.9920   1st Qu.:-0.9929  
##  Median :-0.9513   Median :-0.9440   Median :-0.9187   Median :-0.9380  
##  Mean   :-0.7961   Mean   :-0.7504   Mean   :-0.7925   Mean   :-0.8090  
##  3rd Qu.:-0.6555   3rd Qu.:-0.5243   3rd Qu.:-0.6300   3rd Qu.:-0.6952  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.5985   Max.   : 1.0000  
##                                                                         
##     attr172           attr173           attr174           attr175       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.7598  
##  1st Qu.:-0.9910   1st Qu.: 0.5672   1st Qu.: 0.7280   1st Qu.: 0.6562  
##  Median :-0.9173   Median : 0.9058   Median : 0.9450   Median : 0.9399  
##  Mean   :-0.7473   Mean   : 0.7587   Mean   : 0.8312   Mean   : 0.8017  
##  3rd Qu.:-0.5421   3rd Qu.: 0.9904   3rd Qu.: 0.9939   3rd Qu.: 0.9939  
##  Max.   : 0.9790   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr176           attr177           attr178           attr179       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9932   1st Qu.:-0.9999   1st Qu.:-1.0000   1st Qu.:-0.9999  
##  Median :-0.9439   Median :-0.9958   Median :-0.9981   Median :-0.9974  
##  Mean   :-0.7672   Mean   :-0.9164   Mean   :-0.9385   Mean   :-0.9219  
##  3rd Qu.:-0.5621   3rd Qu.:-0.8737   3rd Qu.:-0.9355   3rd Qu.:-0.8827  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr180           attr181           attr182           attr183         
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.000000  
##  1st Qu.:-0.9915   1st Qu.:-0.9935   1st Qu.:-0.9938   1st Qu.:-0.578014  
##  Median :-0.9420   Median :-0.9633   Median :-0.9597   Median : 0.040187  
##  Mean   :-0.7363   Mean   :-0.8081   Mean   :-0.7695   Mean   :-0.007699  
##  3rd Qu.:-0.4956   3rd Qu.:-0.6706   3rd Qu.:-0.5565   3rd Qu.: 0.544632  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.000000  
##                                                                           
##     attr184             attr185             attr186        
##  Min.   :-1.000000   Min.   :-1.000000   Min.   :-1.00000  
##  1st Qu.:-0.542018   1st Qu.:-0.613102   1st Qu.:-0.12017  
##  Median : 0.058444   Median :-0.056546   Median : 0.02851  
##  Mean   : 0.008778   Mean   :-0.009301   Mean   : 0.04283  
##  3rd Qu.: 0.542262   3rd Qu.: 0.563600   3rd Qu.: 0.20233  
##  Max.   : 0.990820   Max.   : 1.000000   Max.   : 1.00000  
##                                                            
##     attr187            attr188            attr189         
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.000000  
##  1st Qu.:-0.03211   1st Qu.:-0.07668   1st Qu.:-0.005526  
##  Median : 0.08167   Median : 0.07566   Median : 0.145095  
##  Mean   : 0.08427   Mean   : 0.06696   Mean   : 0.136062  
##  3rd Qu.: 0.19782   3rd Qu.: 0.22263   3rd Qu.: 0.291024  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 1.000000  
##                                                           
##     attr190             attr191            attr192        
##  Min.   :-0.984300   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.290848   1st Qu.: 0.01391   1st Qu.:-0.06039  
##  Median :-0.144269   Median : 0.11353   Median : 0.07793  
##  Mean   :-0.138584   Mean   : 0.11311   Mean   : 0.06814  
##  3rd Qu.: 0.003059   3rd Qu.: 0.20781   3rd Qu.: 0.20425  
##  Max.   : 1.000000   Max.   : 1.00000   Max.   : 0.99900  
##                                                           
##     attr193            attr194             attr195        
##  Min.   :-1.00000   Min.   :-1.000000   Min.   :-1.00000  
##  1st Qu.:-0.04813   1st Qu.:-0.224506   1st Qu.:-0.25668  
##  Median : 0.10914   Median :-0.005731   Median :-0.12313  
##  Mean   : 0.10624   Mean   : 0.038275   Mean   :-0.11361  
##  3rd Qu.: 0.26804   3rd Qu.: 0.305453   3rd Qu.: 0.02355  
##  Max.   : 0.95267   Max.   : 0.945532   Max.   : 1.00000  
##                                                           
##     attr196            attr197             attr198        
##  Min.   :-1.00000   Min.   :-1.000000   Min.   :-0.90105  
##  1st Qu.: 0.09854   1st Qu.:-0.008761   1st Qu.:-0.16065  
##  Median : 0.25224   Median : 0.148567   Median : 0.02007  
##  Mean   : 0.24347   Mean   : 0.138984   Mean   : 0.02301  
##  3rd Qu.: 0.40011   3rd Qu.: 0.295033   3rd Qu.: 0.20397  
##  Max.   : 1.00000   Max.   : 1.000000   Max.   : 0.86593  
##                                                           
##     attr199            attr200            attr201           attr202       
##  Min.   :-0.96473   Min.   :-0.95295   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.13219   1st Qu.:-0.27058   1st Qu.:-0.9863   1st Qu.:-0.9854  
##  Median : 0.03762   Median :-0.10468   Median :-0.8451   Median :-0.7945  
##  Mean   : 0.04121   Mean   :-0.10331   Mean   :-0.6276   Mean   :-0.6547  
##  3rd Qu.: 0.21473   3rd Qu.: 0.05908   3rd Qu.:-0.3044   3rd Qu.:-0.3870  
##  Max.   : 1.00000   Max.   : 0.99552   Max.   : 1.0000   Max.   : 0.9284  
##                                                                           
##     attr203           attr204           attr205           attr206       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9872   1st Qu.:-0.9809   1st Qu.:-0.9942   1st Qu.:-0.9863  
##  Median :-0.8084   Median :-0.7484   Median :-0.9658   Median :-0.8451  
##  Mean   :-0.6937   Mean   :-0.5322   Mean   :-0.8647   Mean   :-0.6276  
##  3rd Qu.:-0.4619   3rd Qu.:-0.1304   3rd Qu.:-0.7582   3rd Qu.:-0.3044  
##  Max.   : 0.9080   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr207           attr208           attr209           attr210        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.9998   1st Qu.:-0.9890   1st Qu.:-0.5259   1st Qu.:-0.27357  
##  Median :-0.9826   Median :-0.8505   Median : 0.3319   Median :-0.04842  
##  Mean   :-0.8511   Mean   :-0.7584   Mean   : 0.1669   Mean   :-0.04536  
##  3rd Qu.:-0.7499   3rd Qu.:-0.5893   3rd Qu.: 0.8141   3rd Qu.: 0.17156  
##  Max.   : 1.0000   Max.   : 0.9616   Max.   : 1.0000   Max.   : 1.00000  
##                                                                          
##     attr211              attr212            attr213        
##  Min.   :-1.0000000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.1773982   1st Qu.:-0.03306   1st Qu.:-0.22031  
##  Median :-0.0000395   Median : 0.13905   Median :-0.03845  
##  Mean   : 0.0101903   Mean   : 0.12498   Mean   :-0.03631  
##  3rd Qu.: 0.1851504   3rd Qu.: 0.29511   3rd Qu.: 0.15285  
##  Max.   : 1.0000000   Max.   : 0.98253   Max.   : 0.90313  
##                                                            
##     attr214           attr215           attr216           attr217       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9863   1st Qu.:-0.9854   1st Qu.:-0.9872   1st Qu.:-0.9809  
##  Median :-0.8451   Median :-0.7945   Median :-0.8084   Median :-0.7484  
##  Mean   :-0.6276   Mean   :-0.6547   Mean   :-0.6937   Mean   :-0.5322  
##  3rd Qu.:-0.3044   3rd Qu.:-0.3870   3rd Qu.:-0.4619   3rd Qu.:-0.1304  
##  Max.   : 1.0000   Max.   : 0.9284   Max.   : 0.9080   Max.   : 1.0000  
##                                                                         
##     attr218           attr219           attr220           attr221       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9942   1st Qu.:-0.9863   1st Qu.:-0.9998   1st Qu.:-0.9890  
##  Median :-0.9658   Median :-0.8451   Median :-0.9826   Median :-0.8505  
##  Mean   :-0.8647   Mean   :-0.6276   Mean   :-0.8511   Mean   :-0.7584  
##  3rd Qu.:-0.7582   3rd Qu.:-0.3044   3rd Qu.:-0.7499   3rd Qu.:-0.5893  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9616  
##                                                                         
##     attr222           attr223            attr224          
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.0000000  
##  1st Qu.:-0.5259   1st Qu.:-0.27357   1st Qu.:-0.1773982  
##  Median : 0.3319   Median :-0.04842   Median :-0.0000395  
##  Mean   : 0.1669   Mean   :-0.04536   Mean   : 0.0101903  
##  3rd Qu.: 0.8141   3rd Qu.: 0.17156   3rd Qu.: 0.1851504  
##  Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.0000000  
##                                                           
##     attr225            attr226            attr227           attr228       
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.03306   1st Qu.:-0.22031   1st Qu.:-0.9906   1st Qu.:-0.9908  
##  Median : 0.13905   Median :-0.03845   Median :-0.9346   Median :-0.9056  
##  Mean   : 0.12498   Mean   :-0.03631   Mean   :-0.6551   Mean   :-0.6356  
##  3rd Qu.: 0.29511   3rd Qu.: 0.15285   3rd Qu.:-0.3029   3rd Qu.:-0.2951  
##  Max.   : 0.98253   Max.   : 0.90313   Max.   : 1.0000   Max.   : 1.0000  
##                                                                           
##     attr229           attr230           attr231           attr232       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9913   1st Qu.:-0.9888   1st Qu.:-0.9833   1st Qu.:-0.9906  
##  Median :-0.9182   Median :-0.8997   Median :-0.9578   Median :-0.9346  
##  Mean   :-0.6549   Mean   :-0.6440   Mean   :-0.7893   Mean   :-0.6551  
##  3rd Qu.:-0.3298   3rd Qu.:-0.3142   3rd Qu.:-0.6225   3rd Qu.:-0.3029  
##  Max.   : 1.0000   Max.   : 0.9837   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr233           attr234           attr235            attr236        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.9998   1st Qu.:-0.9922   1st Qu.:-0.80230   1st Qu.:-0.06356  
##  Median :-0.9961   Median :-0.9407   Median :-0.21849   Median : 0.11206  
##  Mean   :-0.8551   Mean   :-0.7058   Mean   :-0.05457   Mean   : 0.10032  
##  3rd Qu.:-0.7388   3rd Qu.:-0.4299   3rd Qu.: 0.69609   3rd Qu.: 0.27808  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.00000   Max.   : 0.82624  
##                                                                           
##     attr237            attr238            attr239        
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.23374   1st Qu.:-0.32941   1st Qu.:-0.09539  
##  Median :-0.06959   Median :-0.18429   Median : 0.05664  
##  Mean   :-0.04273   Mean   :-0.18168   Mean   : 0.05844  
##  3rd Qu.: 0.13465   3rd Qu.:-0.03918   3rd Qu.: 0.21083  
##  Max.   : 0.99510   Max.   : 1.00000   Max.   : 1.00000  
##                                                          
##     attr240           attr241           attr242           attr243       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9784   1st Qu.:-0.9775   1st Qu.:-0.9773   1st Qu.:-0.9808  
##  Median :-0.7463   Median :-0.7735   Median :-0.7642   Median :-0.8014  
##  Mean   :-0.5815   Mean   :-0.6363   Mean   :-0.6233   Mean   :-0.6805  
##  3rd Qu.:-0.2167   3rd Qu.:-0.3515   3rd Qu.:-0.3230   3rd Qu.:-0.4357  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9799  
##                                                                         
##     attr244           attr245           attr246           attr247       
##  Min.   :-0.9999   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9933   1st Qu.:-0.9784   1st Qu.:-0.9996   1st Qu.:-0.9811  
##  Median :-0.9164   Median :-0.7463   Median :-0.9637   Median :-0.7897  
##  Mean   :-0.8339   Mean   :-0.5815   Mean   :-0.8184   Mean   :-0.6661  
##  3rd Qu.:-0.7155   3rd Qu.:-0.2167   3rd Qu.:-0.6794   3rd Qu.:-0.4000  
##  Max.   : 0.9264   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr248            attr249             attr250        
##  Min.   :-0.93849   Min.   :-1.000000   Min.   :-1.00000  
##  1st Qu.:-0.03072   1st Qu.:-0.202013   1st Qu.:-0.37006  
##  Median : 0.37452   Median :-0.009819   Median :-0.19876  
##  Mean   : 0.32016   Mean   :-0.006519   Mean   :-0.18354  
##  3rd Qu.: 0.69117   3rd Qu.: 0.190419   3rd Qu.:-0.01234  
##  Max.   : 1.00000   Max.   : 1.000000   Max.   : 0.93765  
##                                                           
##     attr251            attr252            attr253           attr254       
##  Min.   :-1.00000   Min.   :-0.84977   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.: 0.04818   1st Qu.:-0.19108   1st Qu.:-0.9929   1st Qu.:-0.9926  
##  Median : 0.20104   Median :-0.03058   Median :-0.9419   Median :-0.9205  
##  Mean   : 0.19650   Mean   :-0.02703   Mean   :-0.7622   Mean   :-0.7782  
##  3rd Qu.: 0.35395   3rd Qu.: 0.13740   3rd Qu.:-0.5555   3rd Qu.:-0.6156  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                           
##     attr255           attr256           attr257           attr258       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9933   1st Qu.:-0.9923   1st Qu.:-0.9902   1st Qu.:-0.9929  
##  Median :-0.9311   Median :-0.9218   Median :-0.9662   Median :-0.9419  
##  Mean   :-0.7927   Mean   :-0.7849   Mean   :-0.8054   Mean   :-0.7622  
##  3rd Qu.:-0.6349   3rd Qu.:-0.6403   3rd Qu.:-0.6518   3rd Qu.:-0.5555  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr259           attr260           attr261           attr262       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9941   1st Qu.:-0.5874   1st Qu.: 0.1641  
##  Median :-0.9975   Median :-0.9430   Median : 0.1848   Median : 0.3243  
##  Mean   :-0.9314   Mean   :-0.8060   Mean   : 0.1364   Mean   : 0.3073  
##  3rd Qu.:-0.9045   3rd Qu.:-0.6506   3rd Qu.: 0.8385   3rd Qu.: 0.4718  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr263           attr264            attr265            attr266       
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.0000  
##  1st Qu.:-0.3407   1st Qu.:-0.26625   1st Qu.:-0.18950   1st Qu.:-0.9912  
##  Median :-0.1965   Median :-0.11409   Median :-0.04524   Median :-0.9163  
##  Mean   :-0.1871   Mean   :-0.11597   Mean   :-0.03288   Mean   :-0.6211  
##  3rd Qu.:-0.0499   3rd Qu.: 0.03653   3rd Qu.: 0.11238   3rd Qu.:-0.2689  
##  Max.   : 1.0000   Max.   : 0.85391   Max.   : 0.81403   Max.   : 1.0000  
##                                                                           
##     attr267            attr268           attr269           attr270       
##  Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.97901   1st Qu.:-0.9833   1st Qu.:-0.9924   1st Qu.:-0.9853  
##  Median :-0.80189   Median :-0.8357   Median :-0.9157   Median :-0.8441  
##  Mean   :-0.52151   Mean   :-0.6477   Mean   :-0.5921   Mean   :-0.6838  
##  3rd Qu.:-0.08189   3rd Qu.:-0.3521   3rd Qu.:-0.2416   3rd Qu.:-0.4135  
##  Max.   : 0.97185   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8885  
##                                                                          
##     attr271           attr272           attr273            attr274       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.0000  
##  1st Qu.:-0.9856   1st Qu.:-0.9914   1st Qu.:-0.98020   1st Qu.:-0.9820  
##  Median :-0.8368   Median :-0.9141   Median :-0.79130   Median :-0.8079  
##  Mean   :-0.7284   Mean   :-0.5878   Mean   :-0.50683   Mean   :-0.6099  
##  3rd Qu.:-0.5287   3rd Qu.:-0.2082   3rd Qu.:-0.05846   3rd Qu.:-0.2884  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.94058   Max.   : 1.0000  
##                                                                          
##     attr275           attr276           attr277           attr278       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9939   1st Qu.:-0.9875   1st Qu.:-0.9864   1st Qu.:-0.9945  
##  Median :-0.9161   Median :-0.8653   Median :-0.8612   Median :-0.9715  
##  Mean   :-0.6375   Mean   :-0.7697   Mean   :-0.7894   Mean   :-0.8479  
##  3rd Qu.:-0.3346   3rd Qu.:-0.5967   3rd Qu.:-0.6580   3rd Qu.:-0.7783  
##  Max.   : 1.0000   Max.   : 0.7940   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr279           attr280           attr281           attr282       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9919   1st Qu.:-0.9910   1st Qu.:-0.9859   1st Qu.:-0.9999  
##  Median :-0.9645   Median :-0.9705   Median :-0.8291   Median :-0.9960  
##  Mean   :-0.8685   Mean   :-0.9041   Mean   :-0.5435   Mean   :-0.8212  
##  3rd Qu.:-0.8119   3rd Qu.:-0.8699   3rd Qu.:-0.1143   3rd Qu.:-0.7137  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr283           attr284           attr285           attr286       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9997   1st Qu.:-0.9906   1st Qu.:-0.9870  
##  Median :-0.9841   Median :-0.9833   Median :-0.9262   Median :-0.8989  
##  Mean   :-0.8640   Mean   :-0.8981   Mean   :-0.6591   Mean   :-0.6517  
##  3rd Qu.:-0.7609   3rd Qu.:-0.8442   3rd Qu.:-0.3426   3rd Qu.:-0.3253  
##  Max.   : 0.8938   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr287           attr288           attr289           attr290       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9856   1st Qu.:-0.9464   1st Qu.:-0.8704   1st Qu.:-0.8099  
##  Median :-0.9182   Median :-0.3658   Median :-0.2403   Median :-0.2411  
##  Mean   :-0.7489   Mean   :-0.1920   Mean   :-0.1717   Mean   :-0.1913  
##  3rd Qu.:-0.5466   3rd Qu.: 0.5376   3rd Qu.: 0.4946   3rd Qu.: 0.4018  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9090   Max.   : 1.0000  
##                                                                         
##     attr291           attr292           attr293           attr294        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-0.30980  
##  Median :-0.8000   Median :-0.8667   Median :-0.9231   Median :-0.13670  
##  Mean   :-0.7696   Mean   :-0.8059   Mean   :-0.8541   Mean   :-0.11748  
##  3rd Qu.:-0.7333   3rd Qu.:-0.7333   3rd Qu.:-0.7692   3rd Qu.: 0.08374  
##  Max.   : 0.8667   Max.   : 1.0000   Max.   : 0.9231   Max.   : 1.00000  
##                                                                          
##     attr295            attr296            attr297           attr298       
##  Min.   :-0.93407   Min.   :-1.00000   Min.   :-0.8760   Min.   :-1.0000  
##  1st Qu.:-0.12550   1st Qu.:-0.06645   1st Qu.:-0.4784   1st Qu.:-0.8365  
##  Median : 0.02356   Median : 0.13610   Median :-0.1491   Median :-0.5614  
##  Mean   : 0.02994   Mean   : 0.12067   Mean   :-0.1103   Mean   :-0.4379  
##  3rd Qu.: 0.18580   3rd Qu.: 0.32979   3rd Qu.: 0.1826   3rd Qu.:-0.1453  
##  Max.   : 1.00000   Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                           
##     attr299            attr300           attr301            attr302       
##  Min.   :-0.95782   Min.   :-0.9948   Min.   :-0.93933   Min.   :-0.9958  
##  1st Qu.:-0.56082   1st Qu.:-0.8346   1st Qu.:-0.51953   1st Qu.:-0.8071  
##  Median :-0.38032   Median :-0.6942   Median :-0.26036   Median :-0.5827  
##  Mean   :-0.27032   Mean   :-0.5340   Mean   :-0.18701   Mean   :-0.4528  
##  3rd Qu.:-0.07064   3rd Qu.:-0.3810   3rd Qu.: 0.09572   3rd Qu.:-0.1940  
##  Max.   : 0.98084   Max.   : 0.9748   Max.   : 1.00000   Max.   : 1.0000  
##                                                                           
##     attr303           attr304           attr305           attr306       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999  
##  Median :-0.9960   Median :-0.9982   Median :-0.9969   Median :-0.9965  
##  Mean   :-0.8089   Mean   :-0.8926   Mean   :-0.8637   Mean   :-0.8990  
##  3rd Qu.:-0.7005   3rd Qu.:-0.8329   3rd Qu.:-0.7961   3rd Qu.:-0.8670  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8815  
##                                                                         
##     attr307           attr308           attr309           attr310       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9969   Median :-0.9972   Median :-0.9980   Median :-0.9995  
##  Mean   :-0.9157   Mean   :-0.9129   Mean   :-0.9451   Mean   :-0.9527  
##  3rd Qu.:-0.8802   3rd Qu.:-0.8804   3rd Qu.:-0.9307   3rd Qu.:-0.9673  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr311           attr312           attr313           attr314       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9962   Median :-0.9962   Median :-0.9972   Median :-0.9981  
##  Mean   :-0.8158   Mean   :-0.8529   Mean   :-0.9147   Mean   :-0.9477  
##  3rd Qu.:-0.7102   3rd Qu.:-0.7770   3rd Qu.:-0.8787   3rd Qu.:-0.9400  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr315           attr316           attr317           attr318       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9998  
##  Median :-0.9961   Median :-0.9961   Median :-0.9866   Median :-0.9936  
##  Mean   :-0.8192   Mean   :-0.8869   Mean   :-0.9113   Mean   :-0.8496  
##  3rd Qu.:-0.7113   3rd Qu.:-0.8399   3rd Qu.:-0.8588   3rd Qu.:-0.7731  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8508   Max.   : 0.9500  
##                                                                         
##     attr319           attr320           attr321           attr322       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9996   1st Qu.:-0.9996  
##  Median :-0.9952   Median :-0.9946   Median :-0.9915   Median :-0.9897  
##  Mean   :-0.8652   Mean   :-0.9063   Mean   :-0.8966   Mean   :-0.8798  
##  3rd Qu.:-0.7935   3rd Qu.:-0.8653   3rd Qu.:-0.8468   3rd Qu.:-0.8192  
##  Max.   : 1.0000   Max.   : 0.9581   Max.   : 0.8466   Max.   : 0.8977  
##                                                                         
##     attr323           attr324           attr325           attr326       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-0.9998  
##  Median :-0.9895   Median :-0.9985   Median :-0.9850   Median :-0.9938  
##  Mean   :-0.8964   Mean   :-0.9424   Mean   :-0.8783   Mean   :-0.8427  
##  3rd Qu.:-0.8557   3rd Qu.:-0.9597   3rd Qu.:-0.7909   3rd Qu.:-0.7512  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8701   Max.   : 1.0000  
##                                                                         
##     attr327           attr328           attr329           attr330       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9996   1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9997  
##  Median :-0.9895   Median :-0.9901   Median :-0.9844   Median :-0.9929  
##  Mean   :-0.8783   Mean   :-0.9125   Mean   :-0.8677   Mean   :-0.8928  
##  3rd Qu.:-0.8125   3rd Qu.:-0.8870   3rd Qu.:-0.7684   3rd Qu.:-0.8372  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8810   Max.   : 1.0000  
##                                                                         
##     attr331           attr332           attr333           attr334       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9997   1st Qu.:-0.9998   1st Qu.:-0.9998  
##  Median :-0.9845   Median :-0.9937   Median :-0.9968   Median :-0.9977  
##  Mean   :-0.9255   Mean   :-0.8978   Mean   :-0.9243   Mean   :-0.9605  
##  3rd Qu.:-0.8955   3rd Qu.:-0.8598   3rd Qu.:-0.9109   3rd Qu.:-0.9554  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr335           attr336           attr337           attr338       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9995   1st Qu.:-0.9996   1st Qu.:-0.9999  
##  Median :-0.9968   Median :-0.9928   Median :-0.9918   Median :-0.9982  
##  Mean   :-0.9617   Mean   :-0.9334   Mean   :-0.9365   Mean   :-0.9516  
##  3rd Qu.:-0.9537   3rd Qu.:-0.9142   3rd Qu.:-0.9193   3rd Qu.:-0.9665  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8485  
##                                                                         
##     attr339           attr340           attr341           attr342       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9998   1st Qu.:-0.9997   1st Qu.:-0.9996  
##  Median :-0.9836   Median :-0.9970   Median :-0.9955   Median :-0.9919  
##  Mean   :-0.9094   Mean   :-0.9374   Mean   :-0.9517   Mean   :-0.9393  
##  3rd Qu.:-0.8643   3rd Qu.:-0.9225   3rd Qu.:-0.9387   3rd Qu.:-0.9274  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr343           attr344           attr345           attr346       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9998   1st Qu.:-0.9914   1st Qu.:-0.9851  
##  Median :-0.9833   Median :-0.9970   Median :-0.9382   Median :-0.9041  
##  Mean   :-0.9015   Mean   :-0.9580   Mean   :-0.6647   Mean   :-0.6323  
##  3rd Qu.:-0.8515   3rd Qu.:-0.9486   3rd Qu.:-0.3440   3rd Qu.:-0.2794  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6468  
##                                                                         
##     attr347           attr348           attr349           attr350       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9871   1st Qu.:-0.9921   1st Qu.:-0.9868   1st Qu.:-0.9889  
##  Median :-0.9316   Median :-0.9435   Median :-0.9086   Median :-0.9464  
##  Mean   :-0.7422   Mean   :-0.6657   Mean   :-0.6169   Mean   :-0.7800  
##  3rd Qu.:-0.5232   3rd Qu.:-0.3415   3rd Qu.:-0.2551   3rd Qu.:-0.5999  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr351           attr352           attr353           attr354       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9898   1st Qu.:-0.9867   1st Qu.:-0.9884   1st Qu.:-0.9936  
##  Median :-0.9294   Median :-0.9085   Median :-0.9416   Median :-0.9581  
##  Mean   :-0.6067   Mean   :-0.6288   Mean   :-0.7642   Mean   :-0.7212  
##  3rd Qu.:-0.2195   3rd Qu.:-0.2735   3rd Qu.:-0.5667   3rd Qu.:-0.4601  
##  Max.   : 1.0000   Max.   : 0.8051   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr355           attr356           attr357           attr358       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9882   1st Qu.:-0.9897   1st Qu.:-0.9950   1st Qu.:-0.9912  
##  Median :-0.9273   Median :-0.9522   Median :-0.9815   Median :-0.9683  
##  Mean   :-0.6842   Mean   :-0.8002   Mean   :-0.8837   Mean   :-0.8623  
##  3rd Qu.:-0.4048   3rd Qu.:-0.6479   3rd Qu.:-0.8390   3rd Qu.:-0.8060  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr359           attr360           attr361           attr362       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9883   1st Qu.:-0.9891   1st Qu.:-0.9999   1st Qu.:-0.9998  
##  Median :-0.9683   Median :-0.9149   Median :-0.9977   Median :-0.9944  
##  Mean   :-0.8838   Mean   :-0.6250   Mean   :-0.8561   Mean   :-0.8328  
##  3rd Qu.:-0.8470   3rd Qu.:-0.2577   3rd Qu.:-0.7580   3rd Qu.:-0.7058  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6343  
##                                                                         
##     attr363           attr364           attr365           attr366       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9885   1st Qu.:-0.9884   1st Qu.:-0.9847  
##  Median :-0.9973   Median :-0.9285   Median :-0.9280   Median :-0.9385  
##  Mean   :-0.9297   Mean   :-0.6411   Mean   :-0.7224   Mean   :-0.7696  
##  3rd Qu.:-0.8976   3rd Qu.:-0.3156   3rd Qu.:-0.4630   3rd Qu.:-0.5889  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6413   Max.   : 1.0000  
##                                                                         
##     attr367           attr368           attr369           attr370       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-0.6800  
##  Median :-0.5844   Median :-0.5302   Median :-0.5844   Median :-0.4000  
##  Mean   :-0.2673   Mean   :-0.2576   Mean   :-0.3587   Mean   :-0.4191  
##  3rd Qu.: 0.5061   3rd Qu.: 0.4969   3rd Qu.: 0.2792   3rd Qu.:-0.1600  
##  Max.   : 1.0000   Max.   : 0.9968   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr371           attr372          attr373            attr374        
##  Min.   :-1.0000   Min.   :-1.000   Min.   :-1.00000   Min.   :-1.00000  
##  1st Qu.:-0.5600   1st Qu.:-0.520   1st Qu.:-0.36218   1st Qu.:-0.40069  
##  Median :-0.4000   Median :-0.320   Median :-0.14740   Median :-0.22124  
##  Mean   :-0.4033   Mean   :-0.341   Mean   :-0.13956   Mean   :-0.19676  
##  3rd Qu.:-0.2400   3rd Qu.:-0.160   3rd Qu.: 0.08637   3rd Qu.: 0.01976  
##  Max.   : 1.0000   Max.   : 0.960   Max.   : 1.00000   Max.   : 1.00000  
##                                                                          
##     attr375            attr376           attr377           attr378       
##  Min.   :-1.00000   Min.   :-1.0000   Min.   :-0.9956   Min.   :-1.0000  
##  1st Qu.:-0.16141   1st Qu.:-0.5233   1st Qu.:-0.8751   1st Qu.:-0.5967  
##  Median : 0.03306   Median :-0.3747   Median :-0.7959   Median :-0.4763  
##  Mean   : 0.01899   Mean   :-0.3359   Mean   :-0.7340   Mean   :-0.4533  
##  3rd Qu.: 0.21559   3rd Qu.:-0.1876   3rd Qu.:-0.6611   3rd Qu.:-0.3415  
##  Max.   : 0.96709   Max.   : 0.8278   Max.   : 0.7370   Max.   : 1.0000  
##                                                                          
##     attr379           attr380           attr381           attr382       
##  Min.   :-1.0000   Min.   :-0.9548   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9143   1st Qu.:-0.6025   1st Qu.:-0.9157   1st Qu.:-1.0000  
##  Median :-0.8581   Median :-0.4986   Median :-0.8658   Median :-0.9992  
##  Mean   :-0.8216   Mean   :-0.4653   Mean   :-0.8253   Mean   :-0.8685  
##  3rd Qu.:-0.7748   3rd Qu.:-0.3657   3rd Qu.:-0.7830   3rd Qu.:-0.8077  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr383           attr384           attr385           attr386       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999  
##  Median :-0.9986   Median :-0.9978   Median :-0.9975   Median :-0.9983  
##  Mean   :-0.8937   Mean   :-0.8794   Mean   :-0.9036   Mean   :-0.9238  
##  3rd Qu.:-0.8247   3rd Qu.:-0.8228   3rd Qu.:-0.8746   3rd Qu.:-0.8944  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr387           attr388           attr389           attr390       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9999   1st Qu.:-1.0000   1st Qu.:-1.0000  
##  Median :-0.9981   Median :-0.9988   Median :-0.9999   Median :-0.9987  
##  Mean   :-0.9051   Mean   :-0.9463   Mean   :-0.9847   Mean   :-0.8731  
##  3rd Qu.:-0.8677   3rd Qu.:-0.9285   3rd Qu.:-0.9921   3rd Qu.:-0.7949  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr391           attr392           attr393           attr394       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999  
##  Median :-0.9972   Median :-0.9981   Median :-0.9988   Median :-0.9980  
##  Mean   :-0.8619   Mean   :-0.9098   Mean   :-0.9443   Mean   :-0.8522  
##  3rd Qu.:-0.7935   3rd Qu.:-0.8688   3rd Qu.:-0.9249   3rd Qu.:-0.7465  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr395           attr396           attr397           attr398       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9999   1st Qu.:-0.9998  
##  Median :-0.9967   Median :-0.9913   Median :-0.9964   Median :-0.9959  
##  Mean   :-0.8682   Mean   :-0.8407   Mean   :-0.8713   Mean   :-0.8438  
##  3rd Qu.:-0.8124   3rd Qu.:-0.7205   3rd Qu.:-0.8039   3rd Qu.:-0.7573  
##  Max.   : 1.0000   Max.   : 0.7029   Max.   : 0.8917   Max.   : 0.9084  
##                                                                         
##     attr399           attr400           attr401           attr402       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9997   1st Qu.:-0.9996   1st Qu.:-0.9997  
##  Median :-0.9971   Median :-0.9970   Median :-0.9950   Median :-0.9969  
##  Mean   :-0.9124   Mean   :-0.9174   Mean   :-0.8789   Mean   :-0.9243  
##  3rd Qu.:-0.8752   3rd Qu.:-0.8817   3rd Qu.:-0.8170   3rd Qu.:-0.8927  
##  Max.   : 0.8879   Max.   : 0.6324   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr403           attr404           attr405           attr406       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9996  
##  Median :-0.9995   Median :-0.9943   Median :-0.9955   Median :-0.9954  
##  Mean   :-0.9719   Mean   :-0.8458   Mean   :-0.8447   Mean   :-0.8811  
##  3rd Qu.:-0.9847   3rd Qu.:-0.7472   3rd Qu.:-0.7518   3rd Qu.:-0.8164  
##  Max.   : 1.0000   Max.   : 0.8979   Max.   : 0.9303   Max.   : 1.0000  
##                                                                         
##     attr407           attr408           attr409           attr410       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9997   1st Qu.:-0.9998  
##  Median :-0.9971   Median :-0.9942   Median :-0.9963   Median :-0.9943  
##  Mean   :-0.9303   Mean   :-0.8190   Mean   :-0.8992   Mean   :-0.8983  
##  3rd Qu.:-0.9011   3rd Qu.:-0.6850   3rd Qu.:-0.8445   3rd Qu.:-0.8609  
##  Max.   : 1.0000   Max.   : 0.9149   Max.   : 0.8074   Max.   : 1.0000  
##                                                                         
##     attr411           attr412           attr413           attr414       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9997   1st Qu.:-0.9998   1st Qu.:-0.9998   1st Qu.:-0.9997  
##  Median :-0.9963   Median :-0.9982   Median :-0.9987   Median :-0.9985  
##  Mean   :-0.8995   Mean   :-0.9306   Mean   :-0.9623   Mean   :-0.9661  
##  3rd Qu.:-0.8632   3rd Qu.:-0.9186   3rd Qu.:-0.9579   3rd Qu.:-0.9616  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr415           attr416           attr417           attr418       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9996   1st Qu.:-0.9995   1st Qu.:-0.9999   1st Qu.:-0.9997  
##  Median :-0.9970   Median :-0.9965   Median :-0.9993   Median :-0.9945  
##  Mean   :-0.9403   Mean   :-0.9312   Mean   :-0.9705   Mean   :-0.8779  
##  3rd Qu.:-0.9273   3rd Qu.:-0.9189   3rd Qu.:-0.9872   3rd Qu.:-0.8216  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr419           attr420           attr421           attr422       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9997   1st Qu.:-0.9995   1st Qu.:-0.9997  
##  Median :-0.9984   Median :-0.9980   Median :-0.9965   Median :-0.9963  
##  Mean   :-0.9461   Mean   :-0.9561   Mean   :-0.9314   Mean   :-0.8984  
##  3rd Qu.:-0.9338   3rd Qu.:-0.9464   3rd Qu.:-0.9186   3rd Qu.:-0.8530  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr423           attr424           attr425           attr426       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.9998  
##  1st Qu.:-0.9998   1st Qu.:-0.9851   1st Qu.:-0.9850   1st Qu.:-0.9855  
##  Median :-0.9984   Median :-0.8496   Median :-0.8921   Median :-0.8547  
##  Mean   :-0.9599   Mean   :-0.6638   Mean   :-0.6969   Mean   :-0.6337  
##  3rd Qu.:-0.9516   3rd Qu.:-0.3832   3rd Qu.:-0.4713   3rd Qu.:-0.3103  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr427           attr428           attr429           attr430       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.9999   Min.   :-1.0000  
##  1st Qu.:-0.9878   1st Qu.:-0.9811   1st Qu.:-0.9888   1st Qu.:-0.9868  
##  Median :-0.8658   Median :-0.8739   Median :-0.8789   Median :-0.8567  
##  Mean   :-0.7248   Mean   :-0.6517   Mean   :-0.7243   Mean   :-0.6976  
##  3rd Qu.:-0.5072   3rd Qu.:-0.4082   3rd Qu.:-0.4980   3rd Qu.:-0.4429  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.6510   Max.   : 0.8683  
##                                                                         
##     attr431           attr432           attr433           attr434       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9845   1st Qu.:-0.9855   1st Qu.:-0.9890   1st Qu.:-0.9837  
##  Median :-0.8910   Median :-0.8574   Median :-0.8813   Median :-0.8943  
##  Mean   :-0.6993   Mean   :-0.6254   Mean   :-0.7408   Mean   :-0.7104  
##  3rd Qu.:-0.4817   3rd Qu.:-0.2940   3rd Qu.:-0.5524   3rd Qu.:-0.5322  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.8514   Max.   : 1.0000  
##                                                                         
##     attr435           attr436           attr437           attr438       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9899   1st Qu.:-0.9969   1st Qu.:-0.9947   1st Qu.:-0.9948  
##  Median :-0.8864   Median :-0.9795   Median :-0.9707   Median :-0.9662  
##  Mean   :-0.7624   Mean   :-0.9275   Mean   :-0.8965   Mean   :-0.9006  
##  3rd Qu.:-0.5914   3rd Qu.:-0.9022   3rd Qu.:-0.8585   3rd Qu.:-0.8629  
##  Max.   : 0.8500   Max.   : 0.8437   Max.   : 0.7945   Max.   : 1.0000  
##                                                                         
##     attr439           attr440           attr441           attr442       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9845   1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-0.9999  
##  Median :-0.8630   Median :-0.9901   Median :-0.9925   Median :-0.9906  
##  Mean   :-0.6504   Mean   :-0.9092   Mean   :-0.8748   Mean   :-0.8969  
##  3rd Qu.:-0.3462   3rd Qu.:-0.8573   3rd Qu.:-0.8313   3rd Qu.:-0.8317  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.4207  
##                                                                         
##     attr443           attr444           attr445           attr446        
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.9891   1st Qu.:-0.9904   1st Qu.:-0.9897   1st Qu.:-0.69465  
##  Median :-0.9050   Median :-0.9226   Median :-0.9118   Median :-0.06708  
##  Mean   :-0.7095   Mean   :-0.7525   Mean   :-0.7008   Mean   :-0.08773  
##  3rd Qu.:-0.4663   3rd Qu.:-0.5867   3rd Qu.:-0.4520   3rd Qu.: 0.50721  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.00000  
##                                                                          
##     attr447            attr448           attr449           attr450       
##  Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.64649   1st Qu.:-0.7615   1st Qu.:-1.0000   1st Qu.:-1.0000  
##  Median :-0.03844   Median :-0.1763   Median :-0.9333   Median :-0.9355  
##  Mean   :-0.04036   Mean   :-0.1446   Mean   :-0.8793   Mean   :-0.8166  
##  3rd Qu.: 0.55285   3rd Qu.: 0.4385   3rd Qu.:-0.8667   3rd Qu.:-0.7419  
##  Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.7419  
##                                                                          
##     attr451           attr452            attr453         
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.000000  
##  1st Qu.:-1.0000   1st Qu.:-0.24677   1st Qu.:-0.332434  
##  Median :-0.9355   Median :-0.07822   Median :-0.159970  
##  Mean   :-0.8247   Mean   :-0.08190   Mean   :-0.162796  
##  3rd Qu.:-0.6774   3rd Qu.: 0.08094   3rd Qu.: 0.007678  
##  Max.   : 0.4839   Max.   : 1.00000   Max.   : 0.914039  
##                                                          
##     attr454            attr455            attr456       
##  Min.   :-1.00000   Min.   :-1.00000   Min.   :-1.0000  
##  1st Qu.:-0.27016   1st Qu.:-0.40722   1st Qu.:-0.7450  
##  Median :-0.10019   Median :-0.20910   Median :-0.5718  
##  Mean   :-0.10576   Mean   :-0.16467   Mean   :-0.4809  
##  3rd Qu.: 0.06262   3rd Qu.: 0.04826   3rd Qu.:-0.2938  
##  Max.   : 0.89283   Max.   : 1.00000   Max.   : 1.0000  
##                                                         
##     attr457            attr458           attr459           attr460       
##  Min.   :-1.00000   Min.   :-0.9982   Min.   :-0.9306   Min.   :-0.9938  
##  1st Qu.:-0.44033   1st Qu.:-0.8052   1st Qu.:-0.4740   1st Qu.:-0.7914  
##  Median :-0.22748   Median :-0.6323   Median :-0.2583   Median :-0.6137  
##  Mean   :-0.16296   Mean   :-0.5122   Mean   :-0.1974   Mean   :-0.5033  
##  3rd Qu.: 0.06035   3rd Qu.:-0.3261   3rd Qu.: 0.0444   3rd Qu.:-0.3029  
##  Max.   : 1.00000   Max.   : 1.0000   Max.   : 0.9924   Max.   : 0.9882  
##                                                                          
##     attr461           attr462           attr463           attr464       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9908   Median :-0.9958   Median :-0.9972   Median :-0.9979  
##  Mean   :-0.9229   Mean   :-0.9043   Mean   :-0.9203   Mean   :-0.9598  
##  3rd Qu.:-0.8909   3rd Qu.:-0.8700   3rd Qu.:-0.8936   3rd Qu.:-0.9526  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr465           attr466           attr467           attr468       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9968   Median :-0.9965   Median :-0.9970   Median :-0.9993  
##  Mean   :-0.9501   Mean   :-0.9516   Mean   :-0.9625   Mean   :-0.9738  
##  3rd Qu.:-0.9383   3rd Qu.:-0.9365   3rd Qu.:-0.9582   3rd Qu.:-0.9818  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr469           attr470           attr471           attr472       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9903   Median :-0.9967   Median :-0.9963   Median :-0.9974  
##  Mean   :-0.9135   Mean   :-0.9195   Mean   :-0.9457   Mean   :-0.9675  
##  3rd Qu.:-0.8680   3rd Qu.:-0.8899   3rd Qu.:-0.9311   3rd Qu.:-0.9680  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr473           attr474           attr475           attr476       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-1.0000  
##  Median :-0.9902   Median :-0.9973   Median :-0.9919   Median :-0.9982  
##  Mean   :-0.9106   Mean   :-0.9553   Mean   :-0.8906   Mean   :-0.9565  
##  3rd Qu.:-0.8599   3rd Qu.:-0.9419   3rd Qu.:-0.8613   3rd Qu.:-0.9556  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr477           attr478           attr479           attr480       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-1.0000   1st Qu.:-0.9999  
##  Median :-0.9991   Median :-0.9990   Median :-0.9991   Median :-0.9980  
##  Mean   :-0.9587   Mean   :-0.9670   Mean   :-0.9772   Mean   :-0.9570  
##  3rd Qu.:-0.9669   3rd Qu.:-0.9712   3rd Qu.:-0.9769   3rd Qu.:-0.9545  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr481           attr482           attr483           attr484       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-1.0000   1st Qu.:-0.9998   1st Qu.:-1.0000  
##  Median :-0.9971   Median :-0.9993   Median :-0.9919   Median :-0.9988  
##  Mean   :-0.9508   Mean   :-0.9743   Mean   :-0.8784   Mean   :-0.9513  
##  3rd Qu.:-0.9491   3rd Qu.:-0.9844   3rd Qu.:-0.8370   3rd Qu.:-0.9583  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr485           attr486           attr487           attr488       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-0.9999   1st Qu.:-0.9998   1st Qu.:-1.0000  
##  Median :-0.9988   Median :-0.9969   Median :-0.9920   Median :-0.9988  
##  Mean   :-0.9728   Mean   :-0.9543   Mean   :-0.8673   Mean   :-0.9662  
##  3rd Qu.:-0.9712   3rd Qu.:-0.9542   3rd Qu.:-0.8209   3rd Qu.:-0.9677  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr489           attr490           attr491           attr492       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9919   Median :-0.9972   Median :-0.9978   Median :-0.9985  
##  Mean   :-0.9209   Mean   :-0.9340   Mean   :-0.9322   Mean   :-0.9677  
##  3rd Qu.:-0.8817   3rd Qu.:-0.9163   3rd Qu.:-0.9171   3rd Qu.:-0.9639  
##  Max.   : 0.3517   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr493           attr494           attr495           attr496       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-1.0000  
##  Median :-0.9980   Median :-0.9961   Median :-0.9939   Median :-0.9986  
##  Mean   :-0.9719   Mean   :-0.9606   Mean   :-0.9500   Mean   :-0.9659  
##  3rd Qu.:-0.9669   3rd Qu.:-0.9505   3rd Qu.:-0.9440   3rd Qu.:-0.9777  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr497           attr498           attr499           attr500       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9999  
##  Median :-0.9910   Median :-0.9971   Median :-0.9974   Median :-0.9948  
##  Mean   :-0.9056   Mean   :-0.9197   Mean   :-0.9688   Mean   :-0.9569  
##  3rd Qu.:-0.8500   3rd Qu.:-0.9010   3rd Qu.:-0.9615   3rd Qu.:-0.9557  
##  Max.   : 0.4150   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr501           attr502           attr503           attr504       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9999   1st Qu.:-0.9999   1st Qu.:-0.9840   1st Qu.:-0.9865  
##  Median :-0.9908   Median :-0.9981   Median :-0.7876   Median :-0.8037  
##  Mean   :-0.8992   Mean   :-0.9681   Mean   :-0.5674   Mean   :-0.7077  
##  3rd Qu.:-0.8365   3rd Qu.:-0.9615   3rd Qu.:-0.1962   3rd Qu.:-0.5045  
##  Max.   : 0.4201   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr505           attr506           attr507           attr508       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9810   1st Qu.:-0.9897   1st Qu.:-0.9907   1st Qu.:-0.9840  
##  Median :-0.7585   Median :-0.8480   Median :-0.9599   Median :-0.7876  
##  Mean   :-0.5674   Mean   :-0.7904   Mean   :-0.8707   Mean   :-0.5674  
##  3rd Qu.:-0.2197   3rd Qu.:-0.6639   3rd Qu.:-0.8163   3rd Qu.:-0.1962  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr509           attr510           attr511           attr512       
##  Min.   :-1.0000   Min.   :-0.9996   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9998   1st Qu.:-0.9866   1st Qu.:-0.8735   1st Qu.:-1.0000  
##  Median :-0.9776   Median :-0.8970   Median :-0.2116   Median :-0.8947  
##  Mean   :-0.8738   Mean   :-0.6915   Mean   :-0.1764   Mean   :-0.8199  
##  3rd Qu.:-0.8091   3rd Qu.:-0.4358   3rd Qu.: 0.4860   3rd Qu.:-0.6316  
##  Max.   : 0.8599   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr513            attr514           attr515           attr516       
##  Min.   :-0.94739   Min.   :-0.9964   Min.   :-1.0000   Min.   :-0.9999  
##  1st Qu.:-0.10455   1st Qu.:-0.5746   1st Qu.:-0.8397   1st Qu.:-0.9898  
##  Median : 0.07336   Median :-0.4081   Median :-0.7171   Median :-0.9082  
##  Mean   : 0.07112   Mean   :-0.3179   Mean   :-0.5864   Mean   :-0.6273  
##  3rd Qu.: 0.25305   3rd Qu.:-0.1471   3rd Qu.:-0.4696   3rd Qu.:-0.2798  
##  Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                          
##     attr517           attr518           attr519           attr520       
##  Min.   :-1.0000   Min.   :-0.9997   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9912   1st Qu.:-0.9891   1st Qu.:-0.9928   1st Qu.:-0.9868  
##  Median :-0.9021   Median :-0.8991   Median :-0.9178   Median :-0.9556  
##  Mean   :-0.6501   Mean   :-0.6222   Mean   :-0.6949   Mean   :-0.8079  
##  3rd Qu.:-0.3346   3rd Qu.:-0.2659   3rd Qu.:-0.4373   3rd Qu.:-0.6942  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr521           attr522           attr523           attr524       
##  Min.   :-0.9999   Min.   :-1.0000   Min.   :-0.9999   Min.   :-1.0000  
##  1st Qu.:-0.9898   1st Qu.:-0.9999   1st Qu.:-0.9889   1st Qu.:-1.0000  
##  Median :-0.9082   Median :-0.9945   Median :-0.9237   Median :-0.5539  
##  Mean   :-0.6273   Mean   :-0.8472   Mean   :-0.6817   Mean   :-0.3364  
##  3rd Qu.:-0.2798   3rd Qu.:-0.7462   3rd Qu.:-0.3911   3rd Qu.: 0.3344  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr525           attr526             attr527        
##  Min.   :-1.0000   Min.   :-1.000000   Min.   :-0.99356  
##  1st Qu.:-0.9683   1st Qu.:-0.006938   1st Qu.:-0.59750  
##  Median :-0.9048   Median : 0.158930   Median :-0.35690  
##  Mean   :-0.8826   Mean   : 0.168823   Mean   :-0.30869  
##  3rd Qu.:-0.8730   3rd Qu.: 0.356940   3rd Qu.:-0.07755  
##  Max.   : 1.0000   Max.   : 0.975905   Max.   : 1.00000  
##                                                          
##     attr528           attr529           attr530           attr531       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.8766   1st Qu.:-0.9826   1st Qu.:-0.9781   1st Qu.:-0.9791  
##  Median :-0.7215   Median :-0.8408   Median :-0.7741   Median :-0.7975  
##  Mean   :-0.6112   Mean   :-0.6843   Mean   :-0.6708   Mean   :-0.6654  
##  3rd Qu.:-0.4414   3rd Qu.:-0.4374   3rd Qu.:-0.4226   3rd Qu.:-0.3973  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9593  
##                                                                         
##     attr532           attr533           attr534           attr535       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9809   1st Qu.:-0.9941   1st Qu.:-0.9826   1st Qu.:-0.9997  
##  Median :-0.8066   Median :-0.9566   Median :-0.8408   Median :-0.9736  
##  Mean   :-0.7267   Mean   :-0.8833   Mean   :-0.6843   Mean   :-0.8654  
##  3rd Qu.:-0.5439   3rd Qu.:-0.8357   3rd Qu.:-0.4374   3rd Qu.:-0.7881  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr536           attr537            attr538           attr539        
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.00000  
##  1st Qu.:-0.9856   1st Qu.:-0.66878   1st Qu.:-1.0000   1st Qu.:-0.26017  
##  Median :-0.8849   Median :-0.05799   Median :-0.9487   Median :-0.08424  
##  Mean   :-0.7181   Mean   :-0.06997   Mean   :-0.8918   Mean   :-0.07202  
##  3rd Qu.:-0.4911   3rd Qu.: 0.50655   3rd Qu.:-0.8462   3rd Qu.: 0.11952  
##  Max.   : 1.0000   Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.00000  
##                                                                           
##     attr540            attr541           attr542           attr543       
##  Min.   :-1.00000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.51068   1st Qu.:-0.7988   1st Qu.:-0.9926   1st Qu.:-0.9932  
##  Median :-0.32044   Median :-0.6470   Median :-0.9272   Median :-0.9203  
##  Mean   :-0.26358   Mean   :-0.5555   Mean   :-0.7801   Mean   :-0.7925  
##  3rd Qu.:-0.07023   3rd Qu.:-0.4086   3rd Qu.:-0.6203   3rd Qu.:-0.6518  
##  Max.   : 1.00000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                          
##     attr544           attr545           attr546           attr547       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-0.9924   1st Qu.:-0.9939   1st Qu.:-0.9939   1st Qu.:-0.9926  
##  Median :-0.9157   Median :-0.9286   Median :-0.9691   Median :-0.9272  
##  Mean   :-0.7732   Mean   :-0.8114   Mean   :-0.8724   Mean   :-0.7801  
##  3rd Qu.:-0.6158   3rd Qu.:-0.6961   3rd Qu.:-0.8132   3rd Qu.:-0.6203  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000  
##                                                                         
##     attr548           attr549           attr550           attr551       
##  Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000   Min.   :-1.0000  
##  1st Qu.:-1.0000   1st Qu.:-0.9917   1st Qu.:-0.9557   1st Qu.:-1.0000  
##  Median :-0.9966   Median :-0.9255   Median :-0.3392   Median :-0.9048  
##  Mean   :-0.9375   Mean   :-0.7719   Mean   :-0.2689   Mean   :-0.9038  
##  3rd Qu.:-0.9250   3rd Qu.:-0.6131   3rd Qu.: 0.3261   3rd Qu.:-0.8730  
##  Max.   : 1.0000   Max.   : 1.0000   Max.   : 1.0000   Max.   : 0.9683  
##                                                                         
##     attr552            attr553           attr554           attr555        
##  Min.   :-0.95853   Min.   :-1.0000   Min.   :-1.0000   Min.   :-0.97658  
##  1st Qu.: 0.02031   1st Qu.:-0.5481   1st Qu.:-0.8440   1st Qu.:-0.10823  
##  Median : 0.17082   Median :-0.3540   Median :-0.7101   Median : 0.01763  
##  Mean   : 0.16175   Mean   :-0.3165   Mean   :-0.6251   Mean   : 0.01677  
##  3rd Qu.: 0.31624   3rd Qu.:-0.1375   3rd Qu.:-0.5038   3rd Qu.: 0.16769  
##  Max.   : 1.00000   Max.   : 0.9385   Max.   : 0.9117   Max.   : 1.00000  
##                                                                           
##     attr556            attr557             attr558         
##  Min.   :-1.00000   Min.   :-1.000000   Min.   :-1.000000  
##  1st Qu.:-0.26100   1st Qu.:-0.470267   1st Qu.:-0.373565  
##  Median : 0.02908   Median : 0.001515   Median :-0.005503  
##  Mean   : 0.01847   Mean   : 0.009239   Mean   :-0.005184  
##  3rd Qu.: 0.31488   3rd Qu.: 0.496871   3rd Qu.: 0.352690  
##  Max.   : 1.00000   Max.   : 0.998702   Max.   : 0.991288  
##                                                            
##     attr559           attr560            attr561            targetVar   
##  Min.   :-1.0000   Min.   :-1.00000   Min.   :-0.987874   5      :1423  
##  1st Qu.:-0.8110   1st Qu.:-0.04775   1st Qu.:-0.140560   6      :1413  
##  Median :-0.7066   Median : 0.17678   Median : 0.004583   4      :1293  
##  Mean   :-0.4859   Mean   : 0.05031   Mean   :-0.052888   1      :1226  
##  3rd Qu.:-0.4888   3rd Qu.: 0.24683   3rd Qu.: 0.109507   2      :1073  
##  Max.   : 1.0000   Max.   : 0.48223   Max.   : 1.000000   3      : 987  
##                                                           (Other): 352

2.a.v) Count missing values.

sapply(xy_train, function(x) sum(is.na(x)))
##     attr1     attr2     attr3     attr4     attr5     attr6     attr7 
##         0         0         0         0         0         0         0 
##     attr8     attr9    attr10    attr11    attr12    attr13    attr14 
##         0         0         0         0         0         0         0 
##    attr15    attr16    attr17    attr18    attr19    attr20    attr21 
##         0         0         0         0         0         0         0 
##    attr22    attr23    attr24    attr25    attr26    attr27    attr28 
##         0         0         0         0         0         0         0 
##    attr29    attr30    attr31    attr32    attr33    attr34    attr35 
##         0         0         0         0         0         0         0 
##    attr36    attr37    attr38    attr39    attr40    attr41    attr42 
##         0         0         0         0         0         0         0 
##    attr43    attr44    attr45    attr46    attr47    attr48    attr49 
##         0         0         0         0         0         0         0 
##    attr50    attr51    attr52    attr53    attr54    attr55    attr56 
##         0         0         0         0         0         0         0 
##    attr57    attr58    attr59    attr60    attr61    attr62    attr63 
##         0         0         0         0         0         0         0 
##    attr64    attr65    attr66    attr67    attr68    attr69    attr70 
##         0         0         0         0         0         0         0 
##    attr71    attr72    attr73    attr74    attr75    attr76    attr77 
##         0         0         0         0         0         0         0 
##    attr78    attr79    attr80    attr81    attr82    attr83    attr84 
##         0         0         0         0         0         0         0 
##    attr85    attr86    attr87    attr88    attr89    attr90    attr91 
##         0         0         0         0         0         0         0 
##    attr92    attr93    attr94    attr95    attr96    attr97    attr98 
##         0         0         0         0         0         0         0 
##    attr99   attr100   attr101   attr102   attr103   attr104   attr105 
##         0         0         0         0         0         0         0 
##   attr106   attr107   attr108   attr109   attr110   attr111   attr112 
##         0         0         0         0         0         0         0 
##   attr113   attr114   attr115   attr116   attr117   attr118   attr119 
##         0         0         0         0         0         0         0 
##   attr120   attr121   attr122   attr123   attr124   attr125   attr126 
##         0         0         0         0         0         0         0 
##   attr127   attr128   attr129   attr130   attr131   attr132   attr133 
##         0         0         0         0         0         0         0 
##   attr134   attr135   attr136   attr137   attr138   attr139   attr140 
##         0         0         0         0         0         0         0 
##   attr141   attr142   attr143   attr144   attr145   attr146   attr147 
##         0         0         0         0         0         0         0 
##   attr148   attr149   attr150   attr151   attr152   attr153   attr154 
##         0         0         0         0         0         0         0 
##   attr155   attr156   attr157   attr158   attr159   attr160   attr161 
##         0         0         0         0         0         0         0 
##   attr162   attr163   attr164   attr165   attr166   attr167   attr168 
##         0         0         0         0         0         0         0 
##   attr169   attr170   attr171   attr172   attr173   attr174   attr175 
##         0         0         0         0         0         0         0 
##   attr176   attr177   attr178   attr179   attr180   attr181   attr182 
##         0         0         0         0         0         0         0 
##   attr183   attr184   attr185   attr186   attr187   attr188   attr189 
##         0         0         0         0         0         0         0 
##   attr190   attr191   attr192   attr193   attr194   attr195   attr196 
##         0         0         0         0         0         0         0 
##   attr197   attr198   attr199   attr200   attr201   attr202   attr203 
##         0         0         0         0         0         0         0 
##   attr204   attr205   attr206   attr207   attr208   attr209   attr210 
##         0         0         0         0         0         0         0 
##   attr211   attr212   attr213   attr214   attr215   attr216   attr217 
##         0         0         0         0         0         0         0 
##   attr218   attr219   attr220   attr221   attr222   attr223   attr224 
##         0         0         0         0         0         0         0 
##   attr225   attr226   attr227   attr228   attr229   attr230   attr231 
##         0         0         0         0         0         0         0 
##   attr232   attr233   attr234   attr235   attr236   attr237   attr238 
##         0         0         0         0         0         0         0 
##   attr239   attr240   attr241   attr242   attr243   attr244   attr245 
##         0         0         0         0         0         0         0 
##   attr246   attr247   attr248   attr249   attr250   attr251   attr252 
##         0         0         0         0         0         0         0 
##   attr253   attr254   attr255   attr256   attr257   attr258   attr259 
##         0         0         0         0         0         0         0 
##   attr260   attr261   attr262   attr263   attr264   attr265   attr266 
##         0         0         0         0         0         0         0 
##   attr267   attr268   attr269   attr270   attr271   attr272   attr273 
##         0         0         0         0         0         0         0 
##   attr274   attr275   attr276   attr277   attr278   attr279   attr280 
##         0         0         0         0         0         0         0 
##   attr281   attr282   attr283   attr284   attr285   attr286   attr287 
##         0         0         0         0         0         0         0 
##   attr288   attr289   attr290   attr291   attr292   attr293   attr294 
##         0         0         0         0         0         0         0 
##   attr295   attr296   attr297   attr298   attr299   attr300   attr301 
##         0         0         0         0         0         0         0 
##   attr302   attr303   attr304   attr305   attr306   attr307   attr308 
##         0         0         0         0         0         0         0 
##   attr309   attr310   attr311   attr312   attr313   attr314   attr315 
##         0         0         0         0         0         0         0 
##   attr316   attr317   attr318   attr319   attr320   attr321   attr322 
##         0         0         0         0         0         0         0 
##   attr323   attr324   attr325   attr326   attr327   attr328   attr329 
##         0         0         0         0         0         0         0 
##   attr330   attr331   attr332   attr333   attr334   attr335   attr336 
##         0         0         0         0         0         0         0 
##   attr337   attr338   attr339   attr340   attr341   attr342   attr343 
##         0         0         0         0         0         0         0 
##   attr344   attr345   attr346   attr347   attr348   attr349   attr350 
##         0         0         0         0         0         0         0 
##   attr351   attr352   attr353   attr354   attr355   attr356   attr357 
##         0         0         0         0         0         0         0 
##   attr358   attr359   attr360   attr361   attr362   attr363   attr364 
##         0         0         0         0         0         0         0 
##   attr365   attr366   attr367   attr368   attr369   attr370   attr371 
##         0         0         0         0         0         0         0 
##   attr372   attr373   attr374   attr375   attr376   attr377   attr378 
##         0         0         0         0         0         0         0 
##   attr379   attr380   attr381   attr382   attr383   attr384   attr385 
##         0         0         0         0         0         0         0 
##   attr386   attr387   attr388   attr389   attr390   attr391   attr392 
##         0         0         0         0         0         0         0 
##   attr393   attr394   attr395   attr396   attr397   attr398   attr399 
##         0         0         0         0         0         0         0 
##   attr400   attr401   attr402   attr403   attr404   attr405   attr406 
##         0         0         0         0         0         0         0 
##   attr407   attr408   attr409   attr410   attr411   attr412   attr413 
##         0         0         0         0         0         0         0 
##   attr414   attr415   attr416   attr417   attr418   attr419   attr420 
##         0         0         0         0         0         0         0 
##   attr421   attr422   attr423   attr424   attr425   attr426   attr427 
##         0         0         0         0         0         0         0 
##   attr428   attr429   attr430   attr431   attr432   attr433   attr434 
##         0         0         0         0         0         0         0 
##   attr435   attr436   attr437   attr438   attr439   attr440   attr441 
##         0         0         0         0         0         0         0 
##   attr442   attr443   attr444   attr445   attr446   attr447   attr448 
##         0         0         0         0         0         0         0 
##   attr449   attr450   attr451   attr452   attr453   attr454   attr455 
##         0         0         0         0         0         0         0 
##   attr456   attr457   attr458   attr459   attr460   attr461   attr462 
##         0         0         0         0         0         0         0 
##   attr463   attr464   attr465   attr466   attr467   attr468   attr469 
##         0         0         0         0         0         0         0 
##   attr470   attr471   attr472   attr473   attr474   attr475   attr476 
##         0         0         0         0         0         0         0 
##   attr477   attr478   attr479   attr480   attr481   attr482   attr483 
##         0         0         0         0         0         0         0 
##   attr484   attr485   attr486   attr487   attr488   attr489   attr490 
##         0         0         0         0         0         0         0 
##   attr491   attr492   attr493   attr494   attr495   attr496   attr497 
##         0         0         0         0         0         0         0 
##   attr498   attr499   attr500   attr501   attr502   attr503   attr504 
##         0         0         0         0         0         0         0 
##   attr505   attr506   attr507   attr508   attr509   attr510   attr511 
##         0         0         0         0         0         0         0 
##   attr512   attr513   attr514   attr515   attr516   attr517   attr518 
##         0         0         0         0         0         0         0 
##   attr519   attr520   attr521   attr522   attr523   attr524   attr525 
##         0         0         0         0         0         0         0 
##   attr526   attr527   attr528   attr529   attr530   attr531   attr532 
##         0         0         0         0         0         0         0 
##   attr533   attr534   attr535   attr536   attr537   attr538   attr539 
##         0         0         0         0         0         0         0 
##   attr540   attr541   attr542   attr543   attr544   attr545   attr546 
##         0         0         0         0         0         0         0 
##   attr547   attr548   attr549   attr550   attr551   attr552   attr553 
##         0         0         0         0         0         0         0 
##   attr554   attr555   attr556   attr557   attr558   attr559   attr560 
##         0         0         0         0         0         0         0 
##   attr561 targetVar 
##         0         0

2.a.vi) Summarize the levels of the class attribute.

cbind(freq=table(y_train), percentage=prop.table(table(y_train))*100)
##    freq percentage
## 1  1226 15.7847303
## 2  1073 13.8148577
## 3   987 12.7076091
## 4  1293 16.6473542
## 5  1423 18.3211021
## 6  1413 18.1923523
## 7    47  0.6051242
## 8    23  0.2961246
## 9    75  0.9656238
## 10   60  0.7724990
## 11   90  1.1587486
## 12   57  0.7338741

2.b) Data visualizations

2.b.i) Univariate plots to better understand each attribute.

# Boxplots for each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
    boxplot(x_train[,i], main=names(x_train)[i])
}

# Histograms each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
    hist(x_train[,i], main=names(x_train)[i])
}

# Density plot for each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
    plot(density(x_train[,i]), main=names(x_train)[i])
}

2.b.ii) Multivariate plots to better understand the relationships between attributes

# Scatterplot matrix colored by class
# pairs(targetVar~., data=xy_train, col=xy_train$targetVar)
# Box and whisker plots for each attribute by class
# scales <- list(x=list(relation="free"), y=list(relation="free"))
# featurePlot(x=x_train, y=y_train, plot="box", scales=scales)
# Density plots for each attribute by class value
# featurePlot(x=x_train, y=y_train, plot="density", scales=scales)
# Correlation plot
correlations <- cor(x_train)
corrplot(correlations, method="circle")

email_notify(paste("Data Summarization and Visualization completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6d7b4f4c}"

3. Prepare Data

Some dataset may require additional preparation activities that will best exposes the structure of the problem and the relationships between the input attributes and the output variable. Some data-prep tasks might include:

email_notify(paste("Data Cleaning and Transformation has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@63753b6d}"

3.a) Data Cleaning

# Not applicable for this iteration of the project

3.b) Feature Selection

# Using the correlations calculated previously, we try to find attributes that are highly correlated.
highlyCorrelated <- findCorrelation(correlations, cutoff=0.99)
print(highlyCorrelated)
##   [1]  67  89 168 169 201 206 214 215 219 240 242 245 255 311 312 315 326
##  [18] 329 343 345 346 347 351 352 353 360 407 412 430 473 488 501 516 518
##  [35] 521 524 542 544 547   4   5   6  44  45  46  41  70  71  74  75  76
##  [52]  84  85 124 125 126 164 202 203 204 205 207 208 209 210 211 212 213
##  [69]  96 228 227 229 176 253   7   8   9 266 267 282 283 284  87  88  86
##  [86]  97  98  99 388 361 319 362 334 416 127 128 129 138 440 441 442 216
## [103] 503 241 529 254  42  43
cat('Number of attributes found to be highly correlated:',length(highlyCorrelated))
## Number of attributes found to be highly correlated: 108
# Removing the highly correlated attributes from the training and validation dataframes
xy_train <- xy_train[, -highlyCorrelated]
xy_test <- xy_test[, -highlyCorrelated]

3.c) Data Transforms

# Not applicable for this iteration of the project

3.d) Display the Final Dataset for Model-Building

dim(xy_train)
## [1] 7767  454
dim(xy_test)
## [1] 3162  454
sapply(xy_train, class)
##     attr1     attr2     attr3    attr10    attr11    attr12    attr13 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr14    attr15    attr16    attr17    attr18    attr19    attr20 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr21    attr22    attr23    attr24    attr25    attr26    attr27 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr28    attr29    attr30    attr31    attr32    attr33    attr34 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr35    attr36    attr37    attr38    attr39    attr40    attr47 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr48    attr49    attr50    attr51    attr52    attr53    attr54 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr55    attr56    attr57    attr58    attr59    attr60    attr61 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr62    attr63    attr64    attr65    attr66    attr68    attr69 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr72    attr73    attr77    attr78    attr79    attr80    attr81 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr82    attr83    attr90    attr91    attr92    attr93    attr94 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##    attr95   attr100   attr101   attr102   attr103   attr104   attr105 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr106   attr107   attr108   attr109   attr110   attr111   attr112 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr113   attr114   attr115   attr116   attr117   attr118   attr119 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr120   attr121   attr122   attr123   attr130   attr131   attr132 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr133   attr134   attr135   attr136   attr137   attr139   attr140 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr141   attr142   attr143   attr144   attr145   attr146   attr147 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr148   attr149   attr150   attr151   attr152   attr153   attr154 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr155   attr156   attr157   attr158   attr159   attr160   attr161 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr162   attr163   attr165   attr166   attr167   attr170   attr171 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr172   attr173   attr174   attr175   attr177   attr178   attr179 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr180   attr181   attr182   attr183   attr184   attr185   attr186 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr187   attr188   attr189   attr190   attr191   attr192   attr193 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr194   attr195   attr196   attr197   attr198   attr199   attr200 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr217   attr218   attr220   attr221   attr222   attr223   attr224 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr225   attr226   attr230   attr231   attr232   attr233   attr234 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr235   attr236   attr237   attr238   attr239   attr243   attr244 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr246   attr247   attr248   attr249   attr250   attr251   attr252 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr256   attr257   attr258   attr259   attr260   attr261   attr262 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr263   attr264   attr265   attr268   attr269   attr270   attr271 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr272   attr273   attr274   attr275   attr276   attr277   attr278 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr279   attr280   attr281   attr285   attr286   attr287   attr288 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr289   attr290   attr291   attr292   attr293   attr294   attr295 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr296   attr297   attr298   attr299   attr300   attr301   attr302 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr303   attr304   attr305   attr306   attr307   attr308   attr309 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr310   attr313   attr314   attr316   attr317   attr318   attr320 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr321   attr322   attr323   attr324   attr325   attr327   attr328 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr330   attr331   attr332   attr333   attr335   attr336   attr337 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr338   attr339   attr340   attr341   attr342   attr344   attr348 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr349   attr350   attr354   attr355   attr356   attr357   attr358 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr359   attr363   attr364   attr365   attr366   attr367   attr368 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr369   attr370   attr371   attr372   attr373   attr374   attr375 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr376   attr377   attr378   attr379   attr380   attr381   attr382 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr383   attr384   attr385   attr386   attr387   attr389   attr390 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr391   attr392   attr393   attr394   attr395   attr396   attr397 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr398   attr399   attr400   attr401   attr402   attr403   attr404 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr405   attr406   attr408   attr409   attr410   attr411   attr413 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr414   attr415   attr417   attr418   attr419   attr420   attr421 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr422   attr423   attr424   attr425   attr426   attr427   attr428 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr429   attr431   attr432   attr433   attr434   attr435   attr436 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr437   attr438   attr439   attr443   attr444   attr445   attr446 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr447   attr448   attr449   attr450   attr451   attr452   attr453 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr454   attr455   attr456   attr457   attr458   attr459   attr460 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr461   attr462   attr463   attr464   attr465   attr466   attr467 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr468   attr469   attr470   attr471   attr472   attr474   attr475 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr476   attr477   attr478   attr479   attr480   attr481   attr482 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr483   attr484   attr485   attr486   attr487   attr489   attr490 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr491   attr492   attr493   attr494   attr495   attr496   attr497 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr498   attr499   attr500   attr502   attr504   attr505   attr506 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr507   attr508   attr509   attr510   attr511   attr512   attr513 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr514   attr515   attr517   attr519   attr520   attr522   attr523 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr525   attr526   attr527   attr528   attr530   attr531   attr532 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr533   attr534   attr535   attr536   attr537   attr538   attr539 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr540   attr541   attr543   attr545   attr546   attr548   attr549 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr550   attr551   attr552   attr553   attr554   attr555   attr556 
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" 
##   attr557   attr558   attr559   attr560   attr561 targetVar 
## "numeric" "numeric" "numeric" "numeric" "numeric"  "factor"
email_notify(paste("Data Cleaning and Transformation completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6c3708b3}"
proc.time()-startTimeScript
##    user  system elapsed 
##  173.48  151.82  368.46

4. Model and Evaluate Algorithms

After the data-prep, we next work on finding a workable model by evaluating a subset of machine learning algorithms that are good at exploiting the structure of the training. The typical evaluation tasks include:

For this project, we will evaluate one linear, three non-linear, and three ensemble algorithms:

Linear Algorithm: Linear Discriminant Analysis

Non-Linear Algorithms: Decision Trees (CART) and k-Nearest Neighbors

Ensemble Algorithms: Bagged CART, Random Forest, and Stochastic Gradient Boosting

The random number seed is reset before each run to ensure that the evaluation of each algorithm is performed using the same data splits. It ensures the results are directly comparable.

4.a) Generate models using linear algorithms

# Linear Discriminant Analysis (Classification)
email_notify(paste("Linear Discriminant Analysis modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@eec5a4a}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.lda <- train(targetVar~., data=xy_train, method="lda", metric=metricTarget, trControl=control)
## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear

## Warning in lda.default(x, grouping, ...): variables are collinear
print(fit.lda)
## Linear Discriminant Analysis 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9705206  0.9651129
proc.time()-startTimeModule
##    user  system elapsed 
##   55.04   15.04   21.12
email_notify(paste("Linear Discriminant Analysis modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@1f28c152}"

4.b) Generate models using nonlinear algorithms

# Decision Tree - CART (Regression/Classification)
email_notify(paste("Decision Tree modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@67b92f0a}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.cart <- train(targetVar~., data=xy_train, method="rpart", metric=metricTarget, trControl=control)
print(fit.cart)
## CART 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results across tuning parameters:
## 
##   cp         Accuracy   Kappa     
##   0.1557377  0.5549245  0.46351732
##   0.1927806  0.4727254  0.36048507
##   0.2200504  0.2541464  0.08698281
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.1557377.
proc.time()-startTimeModule
##    user  system elapsed 
##   88.28   10.28   72.78
email_notify(paste("Decision Tree modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@887af79}"
# k-Nearest Neighbors (Regression/Classification)
email_notify(paste("k-Nearest Neighbors modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@23e028a9}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.knn <- train(targetVar~., data=xy_train, method="knn", metric=metricTarget, trControl=control)
print(fit.knn)
## k-Nearest Neighbors 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results across tuning parameters:
## 
##   k  Accuracy   Kappa    
##   5  0.9524956  0.9437625
##   7  0.9496635  0.9404043
##   9  0.9501795  0.9410091
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 5.
proc.time()-startTimeModule
##    user  system elapsed 
## 1335.51    0.64 1336.33
email_notify(paste("k-Nearest Neighbors modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@551aa95a}"

4.c) Generate models using ensemble algorithms

In this section, we will explore the use and tuning of ensemble algorithms to see whether we can improve the results.

# Bagged CART (Regression/Classification)
email_notify(paste("Bagged CART modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3cef309d}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.bagcart <- train(targetVar~., data=xy_train, method="treebag", metric=metricTarget, trControl=control)
print(fit.bagcart)
## Bagged CART 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9573827  0.9495514
proc.time()-startTimeModule
##    user  system elapsed 
## 1744.03  323.78 1176.56
email_notify(paste("Bagged CART modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@4973813a}"
# Random Forest (Regression/Classification)
email_notify(paste("Random Forest modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3224f60b}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.rf <- train(targetVar~., data=xy_train, method="rf", metric=metricTarget, trControl=control)
print(fit.rf)
## Random Forest 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results across tuning parameters:
## 
##   mtry  Accuracy   Kappa    
##     2   0.9518508  0.9429537
##   227   0.9681960  0.9623539
##   453   0.9617590  0.9547282
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 227.
proc.time()-startTimeModule
##    user  system elapsed 
## 6606.78    0.39 6643.89
email_notify(paste("Random Forest modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@26aa12dd}"
# eXtreme Gradient Boosting (Regression/Classification)
email_notify(paste("eXTreme Gradient Boosting modeling has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@d44fc21}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.xgb <- train(targetVar~., data=xy_train, method="xgbTree", metric=metricTarget, trControl=control, verbose=F)
print(fit.xgb)
## eXtreme Gradient Boosting 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results across tuning parameters:
## 
##   eta  max_depth  colsample_bytree  subsample  nrounds  Accuracy 
##   0.3  1          0.6               0.50        50      0.9524919
##   0.3  1          0.6               0.50       100      0.9701318
##   0.3  1          0.6               0.50       150      0.9760549
##   0.3  1          0.6               0.75        50      0.9530059
##   0.3  1          0.6               0.75       100      0.9678124
##   0.3  1          0.6               0.75       150      0.9746379
##   0.3  1          0.6               1.00        50      0.9514636
##   0.3  1          0.6               1.00       100      0.9669123
##   0.3  1          0.6               1.00       150      0.9724488
##   0.3  1          0.8               0.50        50      0.9535202
##   0.3  1          0.8               0.50       100      0.9688404
##   0.3  1          0.8               0.50       150      0.9754084
##   0.3  1          0.8               0.75        50      0.9532618
##   0.3  1          0.8               0.75       100      0.9702571
##   0.3  1          0.8               0.75       150      0.9751522
##   0.3  1          0.8               1.00        50      0.9535194
##   0.3  1          0.8               1.00       100      0.9665254
##   0.3  1          0.8               1.00       150      0.9727052
##   0.3  2          0.6               0.50        50      0.9750192
##   0.3  2          0.6               0.50       100      0.9795286
##   0.3  2          0.6               0.50       150      0.9809434
##   0.3  2          0.6               0.75        50      0.9750225
##   0.3  2          0.6               0.75       100      0.9822327
##   0.3  2          0.6               0.75       150      0.9821033
##   0.3  2          0.6               1.00        50      0.9727045
##   0.3  2          0.6               1.00       100      0.9805564
##   0.3  2          0.6               1.00       150      0.9824881
##   0.3  2          0.8               0.50        50      0.9750183
##   0.3  2          0.8               0.50       100      0.9819731
##   0.3  2          0.8               0.50       150      0.9836477
##   0.3  2          0.8               0.75        50      0.9736051
##   0.3  2          0.8               0.75       100      0.9806865
##   0.3  2          0.8               0.75       150      0.9826173
##   0.3  2          0.8               1.00        50      0.9733475
##   0.3  2          0.8               1.00       100      0.9799141
##   0.3  2          0.8               1.00       150      0.9819720
##   0.3  3          0.6               0.50        50      0.9778562
##   0.3  3          0.6               0.50       100      0.9823611
##   0.3  3          0.6               0.50       150      0.9831334
##   0.3  3          0.6               0.75        50      0.9800421
##   0.3  3          0.6               0.75       100      0.9828754
##   0.3  3          0.6               0.75       150      0.9830041
##   0.3  3          0.6               1.00        50      0.9795257
##   0.3  3          0.6               1.00       100      0.9841609
##   0.3  3          0.6               1.00       150      0.9846770
##   0.3  3          0.8               0.50        50      0.9768236
##   0.3  3          0.8               0.50       100      0.9800418
##   0.3  3          0.8               0.50       150      0.9814587
##   0.3  3          0.8               0.75        50      0.9790140
##   0.3  3          0.8               0.75       100      0.9824868
##   0.3  3          0.8               0.75       150      0.9826158
##   0.3  3          0.8               1.00        50      0.9801713
##   0.3  3          0.8               1.00       100      0.9830041
##   0.3  3          0.8               1.00       150      0.9833905
##   0.4  1          0.6               0.50        50      0.9593091
##   0.4  1          0.6               0.50       100      0.9711576
##   0.4  1          0.6               0.50       150      0.9756661
##   0.4  1          0.6               0.75        50      0.9576386
##   0.4  1          0.6               0.75       100      0.9736066
##   0.4  1          0.6               0.75       150      0.9774690
##   0.4  1          0.6               1.00        50      0.9586730
##   0.4  1          0.6               1.00       100      0.9705170
##   0.4  1          0.6               1.00       150      0.9751515
##   0.4  1          0.8               0.50        50      0.9598315
##   0.4  1          0.8               0.50       100      0.9743775
##   0.4  1          0.8               0.50       150      0.9772101
##   0.4  1          0.8               0.75        50      0.9586674
##   0.4  1          0.8               0.75       100      0.9718046
##   0.4  1          0.8               0.75       150      0.9760517
##   0.4  1          0.8               1.00        50      0.9584155
##   0.4  1          0.8               1.00       100      0.9696182
##   0.4  1          0.8               1.00       150      0.9755383
##   0.4  2          0.6               0.50        50      0.9748919
##   0.4  2          0.6               0.50       100      0.9795262
##   0.4  2          0.6               0.50       150      0.9812004
##   0.4  2          0.6               0.75        50      0.9756652
##   0.4  2          0.6               0.75       100      0.9818443
##   0.4  2          0.6               0.75       150      0.9827453
##   0.4  2          0.6               1.00        50      0.9760496
##   0.4  2          0.6               1.00       100      0.9804272
##   0.4  2          0.6               1.00       150      0.9821017
##   0.4  2          0.8               0.50        50      0.9751508
##   0.4  2          0.8               0.50       100      0.9799152
##   0.4  2          0.8               0.50       150      0.9813315
##   0.4  2          0.8               0.75        50      0.9766946
##   0.4  2          0.8               0.75       100      0.9811988
##   0.4  2          0.8               0.75       150      0.9818433
##   0.4  2          0.8               1.00        50      0.9765675
##   0.4  2          0.8               1.00       100      0.9824891
##   0.4  2          0.8               1.00       150      0.9828757
##   0.4  3          0.6               0.50        50      0.9791434
##   0.4  3          0.6               0.50       100      0.9815895
##   0.4  3          0.6               0.50       150      0.9817182
##   0.4  3          0.6               0.75        50      0.9797821
##   0.4  3          0.6               0.75       100      0.9824871
##   0.4  3          0.6               0.75       150      0.9828735
##   0.4  3          0.6               1.00        50      0.9815869
##   0.4  3          0.6               1.00       100      0.9832605
##   0.4  3          0.6               1.00       150      0.9837749
##   0.4  3          0.8               0.50        50      0.9799136
##   0.4  3          0.8               0.50       100      0.9814593
##   0.4  3          0.8               0.50       150      0.9826171
##   0.4  3          0.8               0.75        50      0.9803012
##   0.4  3          0.8               0.75       100      0.9833892
##   0.4  3          0.8               0.75       150      0.9837754
##   0.4  3          0.8               1.00        50      0.9804266
##   0.4  3          0.8               1.00       100      0.9824854
##   0.4  3          0.8               1.00       150      0.9831296
##   Kappa    
##   0.9437457
##   0.9646433
##   0.9716567
##   0.9443673
##   0.9618960
##   0.9699769
##   0.9425386
##   0.9608324
##   0.9673851
##   0.9449755
##   0.9631143
##   0.9708900
##   0.9446654
##   0.9647912
##   0.9705869
##   0.9449708
##   0.9603752
##   0.9676900
##   0.9704280
##   0.9757705
##   0.9774434
##   0.9704311
##   0.9789695
##   0.9788170
##   0.9676905
##   0.9769850
##   0.9792729
##   0.9704265
##   0.9786628
##   0.9806467
##   0.9687566
##   0.9771390
##   0.9794247
##   0.9684500
##   0.9762258
##   0.9786610
##   0.9737913
##   0.9791248
##   0.9800398
##   0.9763749
##   0.9797309
##   0.9798840
##   0.9757649
##   0.9812519
##   0.9818643
##   0.9725681
##   0.9763792
##   0.9780564
##   0.9751594
##   0.9792710
##   0.9794250
##   0.9765314
##   0.9798839
##   0.9803404
##   0.9518209
##   0.9658568
##   0.9711954
##   0.9498433
##   0.9687575
##   0.9733269
##   0.9510739
##   0.9651004
##   0.9705869
##   0.9524426
##   0.9696682
##   0.9730247
##   0.9510631
##   0.9666264
##   0.9716506
##   0.9507655
##   0.9640355
##   0.9710454
##   0.9702798
##   0.9757701
##   0.9777515
##   0.9711951
##   0.9785102
##   0.9795773
##   0.9716503
##   0.9768332
##   0.9788159
##   0.9705880
##   0.9762279
##   0.9779041
##   0.9724119
##   0.9777471
##   0.9785104
##   0.9722621
##   0.9792732
##   0.9797312
##   0.9753129
##   0.9782098
##   0.9783625
##   0.9760693
##   0.9792723
##   0.9797305
##   0.9782038
##   0.9801874
##   0.9807965
##   0.9762250
##   0.9780560
##   0.9794257
##   0.9766824
##   0.9803385
##   0.9807959
##   0.9768308
##   0.9792696
##   0.9800321
## 
## Tuning parameter 'gamma' was held constant at a value of 0
## 
## Tuning parameter 'min_child_weight' was held constant at a value of 1
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were nrounds = 150, max_depth = 3,
##  eta = 0.3, gamma = 0, colsample_bytree = 0.6, min_child_weight = 1
##  and subsample = 1.
proc.time()-startTimeModule
##     user   system  elapsed 
## 59513.88 13944.00 24174.34
email_notify(paste("eXtreme Gradient Boosting modeling completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@48503868}"

4.d) Compare baseline algorithms

results <- resamples(list(LDA=fit.lda, CART=fit.cart, kNN=fit.knn, BagCART=fit.bagcart, RF=fit.rf, XGB=fit.xgb))
summary(results)
## 
## Call:
## summary.resamples(object = results)
## 
## Models: LDA, CART, kNN, BagCART, RF, XGB 
## Number of resamples: 10 
## 
## Accuracy 
##              Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## LDA     0.9627249 0.9661963 0.9703591 0.9705206 0.9726694 0.9832041    0
## CART    0.5155039 0.5199614 0.5212082 0.5549245 0.6019210 0.6447876    0
## kNN     0.9447301 0.9488093 0.9511890 0.9524956 0.9580245 0.9601030    0
## BagCART 0.9535484 0.9543279 0.9568855 0.9573827 0.9596785 0.9626770    0
## RF      0.9612903 0.9645377 0.9684685 0.9681960 0.9711069 0.9768638    0
## XGB     0.9806202 0.9819587 0.9851995 0.9846770 0.9867879 0.9897172    0
## 
## Kappa 
##              Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## LDA     0.9559162 0.9599934 0.9649273 0.9651129 0.9676571 0.9801149    0
## CART    0.4155538 0.4205542 0.4226051 0.4635173 0.5206975 0.5730081    0
## kNN     0.9345629 0.9394042 0.9422239 0.9437625 0.9502767 0.9527861    0
## BagCART 0.9449711 0.9459949 0.9489542 0.9495514 0.9522539 0.9558024    0
## RF      0.9541918 0.9580087 0.9626630 0.9623539 0.9658218 0.9726105    0
## XGB     0.9770536 0.9786358 0.9824821 0.9818643 0.9843720 0.9878313    0
dotplot(results)

cat('The average accuracy from all models is:',
    mean(c(results$values$`LDA~Accuracy`,results$values$`CART~Accuracy`,results$values$`kNN~Accuracy`,results$values$`BagCART~Accuracy`,results$values$`RF~Accuracy`,results$values$`XGB~Accuracy`)))
## The average accuracy from all models is: 0.8980327

5. Improve Accuracy or Results

After we achieve a short list of machine learning algorithms with good level of accuracy, we can leverage ways to improve the accuracy of the models.

Using the three best-perfoming algorithms from the previous section, we will Search for a combination of parameters for each algorithm that yields the best results.

5.a) Algorithm Tuning

Finally, we will tune the best-performing algorithms from each group further and see whether we can get more accuracy out of them.

# Tuning algorithm #1 - Linear Discriminant Analysis
# Linear Discriminant Analysis has no special tuning parameters
email_notify(paste("Algorithm #1 tuning has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@396f6598}"
startTimeModule <- proc.time()
set.seed(seedNum)
fit.final1 <- fit.lda
print(fit.final1)
## Linear Discriminant Analysis 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.9705206  0.9651129
proc.time()-startTimeModule
##    user  system elapsed 
##    0.02    0.00    0.01
email_notify(paste("Algorithm #1 tuning completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@1e965684}"
# Tuning algorithm #2 - eXtreme Gradient Boosting
email_notify(paste("Algorithm #2 tuning has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@15d0c81b}"
startTimeModule <- proc.time()
set.seed(seedNum)
grid <- expand.grid(nrounds = c(450,600,750), max_depth = 3, eta = 0.3, gamma = 0, colsample_bytree = 0.6, min_child_weight = 1, subsample = 1)
fit.final2 <- train(targetVar~., data=xy_train, method="xgbTree", metric=metricTarget, tuneGrid=grid, trControl=control, verbose=F)
plot(fit.final2)

print(fit.final2)
## eXtreme Gradient Boosting 
## 
## 7767 samples
##  453 predictor
##   12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times) 
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ... 
## Resampling results across tuning parameters:
## 
##   nrounds  Accuracy   Kappa    
##   450      0.9846765  0.9818639
##   600      0.9849336  0.9821684
##   750      0.9850626  0.9823212
## 
## Tuning parameter 'max_depth' was held constant at a value of 3
##  0.6
## Tuning parameter 'min_child_weight' was held constant at a value of
##  1
## Tuning parameter 'subsample' was held constant at a value of 1
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were nrounds = 750, max_depth = 3,
##  eta = 0.3, gamma = 0, colsample_bytree = 0.6, min_child_weight = 1
##  and subsample = 1.
proc.time()-startTimeModule
##    user  system elapsed 
## 5807.17 1838.72 3137.36
email_notify(paste("Algorithm #2 tuning completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@536aaa8d}"

5.d) Compare Algorithms After Tuning

results <- resamples(list(LDA=fit.final1, XGB=fit.final2))
summary(results)
## 
## Call:
## summary.resamples(object = results)
## 
## Models: LDA, XGB 
## Number of resamples: 10 
## 
## Accuracy 
##          Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## LDA 0.9627249 0.9661963 0.9703591 0.9705206 0.9726694 0.9832041    0
## XGB 0.9832041 0.9832690 0.9845361 0.9850626 0.9864914 0.9897172    0
## 
## Kappa 
##          Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## LDA 0.9559162 0.9599934 0.9649273 0.9651129 0.9676571 0.9801149    0
## XGB 0.9801079 0.9801961 0.9816933 0.9823212 0.9840134 0.9878313    0
dotplot(results)

6. Finalize Model and Present Results

Once we have narrow down to a model that we believe can make accurate predictions on unseen data, we are ready to finalize it. Finalizing a model may involve sub-tasks such as:

email_notify(paste("Model Validation and Final Model Creation has begun!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@4493d195}"

6.a) Predictions on validation dataset

predictions <- predict(fit.final2, newdata=x_test)
confusionMatrix(predictions, y_test$targetVar)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   1   2   3   4   5   6   7   8   9  10  11  12
##         1  488  19   4   0   0   0   0   0   0   0   2   0
##         2    6 447  23   0   0   0   1   0   0   0   0   0
##         3    2   5 393   0   0   0   0   0   0   0   0   0
##         4    0   0   0 455  28   0   1   0   0   0   1   0
##         5    0   0   0  50 527   0   1   0   0   0   0   0
##         6    0   0   0   0   0 545   0   0   0   0   0   0
##         7    0   0   0   2   0   0  19   0   0   0   1   1
##         8    0   0   0   1   0   0   0  10   0   1   0   0
##         9    0   0   0   0   0   0   0   0  26   0   8   0
##         10   0   0   0   0   0   0   0   0   0  18   0   8
##         11   0   0   0   0   1   0   1   0   6   0  36   2
##         12   0   0   0   0   0   0   0   0   0   6   1  16
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9424          
##                  95% CI : (0.9337, 0.9503)
##     No Information Rate : 0.1758          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9321          
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6
## Sensitivity            0.9839   0.9490   0.9357   0.8957   0.9478   1.0000
## Specificity            0.9906   0.9889   0.9974   0.9887   0.9804   1.0000
## Pos Pred Value         0.9513   0.9371   0.9825   0.9381   0.9118   1.0000
## Neg Pred Value         0.9970   0.9911   0.9902   0.9802   0.9888   1.0000
## Prevalence             0.1569   0.1490   0.1328   0.1607   0.1758   0.1724
## Detection Rate         0.1543   0.1414   0.1243   0.1439   0.1667   0.1724
## Detection Prevalence   0.1622   0.1509   0.1265   0.1534   0.1828   0.1724
## Balanced Accuracy      0.9872   0.9689   0.9666   0.9422   0.9641   1.0000
##                      Class: 7 Class: 8 Class: 9 Class: 10 Class: 11
## Sensitivity          0.826087 1.000000 0.812500  0.720000   0.73469
## Specificity          0.998726 0.999365 0.997444  0.997450   0.99679
## Pos Pred Value       0.826087 0.833333 0.764706  0.692308   0.78261
## Neg Pred Value       0.998726 1.000000 0.998082  0.997768   0.99583
## Prevalence           0.007274 0.003163 0.010120  0.007906   0.01550
## Detection Rate       0.006009 0.003163 0.008223  0.005693   0.01139
## Detection Prevalence 0.007274 0.003795 0.010753  0.008223   0.01455
## Balanced Accuracy    0.912406 0.999683 0.904972  0.858725   0.86574
##                      Class: 12
## Sensitivity           0.592593
## Specificity           0.997767
## Pos Pred Value        0.695652
## Neg Pred Value        0.996496
## Prevalence            0.008539
## Detection Rate        0.005060
## Detection Prevalence  0.007274
## Balanced Accuracy     0.795180

6.b) Create standalone model on entire training dataset

startTimeModule <- proc.time()
set.seed(seedNum)
#library(xgboost)

# Combining the training and test datasets to form the original dataset that will be used for training the final model
#xy_complete <- rbind(xy_train, xy_test)
#totCol <- ncol(xy_complete)
#x_complete <- xy_complete[,1:totCol]
#y_complete <- xy_complete[,totCol]
#dataMatrix <- data.matrix(x_complete)
#labelMatrix <- data.matrix(y_complete)

#finalModel <- xgboost(data=dataMatrix, label=labelMatrix, nrounds = 600, max_depth = 3, eta = 0.3, gamma = 0, colsample_bytree = 0.6, min_child_weight = 1, subsample = 1, verbosity=0)
#summary(finalModel)
proc.time()-startTimeModule
##    user  system elapsed 
##       0       0       0

6.c) Save model for later use

#saveRDS(finalModel, "./finalModel_MultiClass.rds")
email_notify(paste("Model Validation and Final Model Creation Completed!",date()))
## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@458c1321}"
proc.time()-startTimeScript
##     user   system  elapsed 
## 75332.03 16285.14 37044.58